2896 lines
106 KiB
Coq
Executable File
2896 lines
106 KiB
Coq
Executable File
Require Import Coq.ZArith.ZArith.
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Require Import Coq.Bool.Bool.
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Require Import Coq.Strings.String.
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Require Import Coq.Lists.List.
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Require Import Coq.Classes.RelationClasses.
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Require Import Coq.Classes.Morphisms.
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Require Import Coq.micromega.Psatz.
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Require Import Coq.Sorting.Permutation.
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From AUXLib Require Import int_auto Axioms Feq Idents List_lemma VMap.
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Require Import SetsClass.SetsClass. Import SetsNotation.
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From SimpleC.SL Require Import Mem SeparationLogic.
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Require Import Logic.LogicGenerator.demo932.Interface.
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Require Import GmpLib.GmpNumber. Import Internal.
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Local Open Scope Z_scope.
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Local Open Scope sets.
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Local Open Scope string.
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Local Open Scope list.
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Import naive_C_Rules.
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Local Open Scope sac.
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Definition Zmax := Z.max.
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(*----- Function gmp_abs -----*)
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Definition gmp_abs_safety_wit_1 :=
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forall (x_pre: Z) ,
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[| (x_pre < 0) |]
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&& [| (INT_MIN < x_pre) |]
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&& [| (x_pre <= INT_MAX) |]
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&& ((( &( "x" ) )) # Int |-> x_pre)
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|--
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[| (x_pre <> (INT_MIN)) |]
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.
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Definition gmp_abs_return_wit_1_1 :=
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forall (x_pre: Z) ,
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[| (x_pre < 0) |]
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&& [| (INT_MIN < x_pre) |]
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&& [| (x_pre <= INT_MAX) |]
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&& emp
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|--
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[| ((-x_pre) = (Zabs (x_pre))) |]
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&& emp
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.
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Definition gmp_abs_return_wit_1_2 :=
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forall (x_pre: Z) ,
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[| (x_pre >= 0) |]
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&& [| (INT_MIN < x_pre) |]
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&& [| (x_pre <= INT_MAX) |]
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&& emp
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|--
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[| (x_pre = (Zabs (x_pre))) |]
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&& emp
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.
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(*----- Function gmp_max -----*)
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Definition gmp_max_return_wit_1_1 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre <= b_pre) |]
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&& emp
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|--
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[| (b_pre = (Zmax (a_pre) (b_pre))) |]
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&& emp
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.
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Definition gmp_max_return_wit_1_2 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre > b_pre) |]
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&& emp
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|--
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[| (a_pre = (Zmax (a_pre) (b_pre))) |]
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&& emp
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.
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(*----- Function gmp_cmp -----*)
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Definition gmp_cmp_safety_wit_1 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre >= b_pre) |]
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&& [| (a_pre <= b_pre) |]
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&& ((( &( "b" ) )) # Int |-> b_pre)
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** ((( &( "a" ) )) # Int |-> a_pre)
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|--
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[| ((0 - 0 ) <= INT_MAX) |]
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&& [| ((INT_MIN) <= (0 - 0 )) |]
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.
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Definition gmp_cmp_safety_wit_2 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre < b_pre) |]
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&& [| (a_pre <= b_pre) |]
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&& ((( &( "b" ) )) # Int |-> b_pre)
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** ((( &( "a" ) )) # Int |-> a_pre)
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|--
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[| ((0 - 1 ) <= INT_MAX) |]
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&& [| ((INT_MIN) <= (0 - 1 )) |]
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.
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Definition gmp_cmp_safety_wit_3 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre >= b_pre) |]
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&& [| (a_pre > b_pre) |]
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&& ((( &( "b" ) )) # Int |-> b_pre)
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** ((( &( "a" ) )) # Int |-> a_pre)
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|--
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[| ((1 - 0 ) <= INT_MAX) |]
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&& [| ((INT_MIN) <= (1 - 0 )) |]
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.
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Definition gmp_cmp_safety_wit_4 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre < b_pre) |]
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&& [| (a_pre > b_pre) |]
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&& ((( &( "b" ) )) # Int |-> b_pre)
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** ((( &( "a" ) )) # Int |-> a_pre)
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|--
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[| False |]
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.
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Definition gmp_cmp_return_wit_1_1 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre >= b_pre) |]
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&& [| (a_pre > b_pre) |]
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&& emp
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|--
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([| (a_pre < b_pre) |]
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&& [| ((1 - 0 ) = (-1)) |]
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&& emp)
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||
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([| (a_pre = b_pre) |]
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&& [| ((1 - 0 ) = 0) |]
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&& emp)
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||
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([| (a_pre > b_pre) |]
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&& [| ((1 - 0 ) = 1) |]
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&& emp)
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.
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Definition gmp_cmp_return_wit_1_2 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre < b_pre) |]
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&& [| (a_pre <= b_pre) |]
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&& emp
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|--
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([| (a_pre < b_pre) |]
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&& [| ((0 - 1 ) = (-1)) |]
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&& emp)
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||
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([| (a_pre = b_pre) |]
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&& [| ((0 - 1 ) = 0) |]
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&& emp)
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||
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([| (a_pre > b_pre) |]
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&& [| ((0 - 1 ) = 1) |]
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&& emp)
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.
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Definition gmp_cmp_return_wit_1_3 :=
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forall (b_pre: Z) (a_pre: Z) ,
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[| (a_pre >= b_pre) |]
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&& [| (a_pre <= b_pre) |]
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&& emp
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|--
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([| (a_pre < b_pre) |]
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&& [| ((0 - 0 ) = (-1)) |]
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&& emp)
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||
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([| (a_pre = b_pre) |]
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&& [| ((0 - 0 ) = 0) |]
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&& emp)
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||
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([| (a_pre > b_pre) |]
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&& [| ((0 - 0 ) = 1) |]
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&& emp)
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.
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(*----- Function mpn_copyi -----*)
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Definition mpn_copyi_safety_wit_1 :=
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forall (n_pre: Z) (s_pre: Z) (d_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) ,
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[| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& ((( &( "i" ) )) # Int |->_)
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** ((( &( "d" ) )) # Ptr |-> d_pre)
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** (store_uint_array_rec d_pre 0 cap2 l2 )
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** (store_uint_array d_pre 0 nil )
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** ((( &( "n" ) )) # Int |-> n_pre)
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** ((( &( "s" ) )) # Ptr |-> s_pre)
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** (store_uint_array s_pre n_pre l )
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** (store_undef_uint_array_rec s_pre n_pre cap1 )
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|--
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[| (0 <= INT_MAX) |]
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&& [| ((INT_MIN) <= 0) |]
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.
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Definition mpn_copyi_safety_wit_2 :=
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forall (n_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (l': (@list Z)) (d: Z) (s: Z) (l_2: (@list Z)) (n: Z) (i: Z) (a: Z) (l2': (@list Z)) ,
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[| (l' = (cons (a) (l2'))) |]
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&& [| (i < n) |]
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&& [| (n <= cap2) |]
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&& [| (i < n) |]
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&& [| (0 <= i) |]
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&& [| (i <= n) |]
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&& [| ((Zlength (l_2)) = n) |]
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&& [| (list_store_Z l_2 val ) |]
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&& [| (n <= cap1) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array d (i + 1 ) (replace_Znth (i) ((Znth i l_2 0)) ((app ((sublist (0) (i) (l_2))) ((cons (a) (nil)))))) )
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** (store_uint_array s n l_2 )
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** ((( &( "i" ) )) # Int |-> i)
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** ((( &( "n" ) )) # Int |-> n)
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** ((( &( "d" ) )) # Ptr |-> d)
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** (store_uint_array_rec d (i + 1 ) cap2 l2' )
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** ((( &( "s" ) )) # Ptr |-> s)
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** (store_undef_uint_array_rec s n cap1 )
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|--
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[| ((i + 1 ) <= INT_MAX) |]
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&& [| ((INT_MIN) <= (i + 1 )) |]
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.
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Definition mpn_copyi_entail_wit_1 :=
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forall (n_pre: Z) (s_pre: Z) (d_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) ,
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[| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l_2)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l_2 val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array_rec d_pre 0 cap2 l2 )
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** (store_uint_array d_pre 0 nil )
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** (store_uint_array s_pre n_pre l_2 )
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** (store_undef_uint_array_rec s_pre n_pre cap1 )
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|--
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EX (l': (@list Z)) (l: (@list Z)) ,
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[| (0 <= 0) |]
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&& [| (0 <= n_pre) |]
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&& [| ((Zlength (l)) = n_pre) |]
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&& [| (list_store_Z l val ) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l_2)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l_2 val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array s_pre n_pre l )
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** (store_undef_uint_array_rec s_pre n_pre cap1 )
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** (store_uint_array d_pre 0 (sublist (0) (0) (l)) )
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** (store_uint_array_rec d_pre 0 cap2 l' )
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.
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Definition mpn_copyi_entail_wit_2 :=
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forall (n_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (l'_2: (@list Z)) (d: Z) (s: Z) (l_3: (@list Z)) (n: Z) (i: Z) (a: Z) (l2': (@list Z)) ,
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[| (l'_2 = (cons (a) (l2'))) |]
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&& [| (i < n) |]
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&& [| (n <= cap2) |]
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&& [| (i < n) |]
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&& [| (0 <= i) |]
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&& [| (i <= n) |]
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&& [| ((Zlength (l_3)) = n) |]
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&& [| (list_store_Z l_3 val ) |]
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&& [| (n <= cap1) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l_2)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l_2 val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array d (i + 1 ) (replace_Znth (i) ((Znth i l_3 0)) ((app ((sublist (0) (i) (l_3))) ((cons (a) (nil)))))) )
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** (store_uint_array s n l_3 )
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** (store_uint_array_rec d (i + 1 ) cap2 l2' )
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** (store_undef_uint_array_rec s n cap1 )
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|--
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EX (l': (@list Z)) (l: (@list Z)) ,
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[| (0 <= (i + 1 )) |]
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&& [| ((i + 1 ) <= n) |]
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&& [| ((Zlength (l)) = n) |]
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&& [| (list_store_Z l val ) |]
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&& [| (n <= cap1) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l_2)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l_2 val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array s n l )
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** (store_undef_uint_array_rec s n cap1 )
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** (store_uint_array d (i + 1 ) (sublist (0) ((i + 1 )) (l)) )
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** (store_uint_array_rec d (i + 1 ) cap2 l' )
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.
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Definition mpn_copyi_return_wit_1 :=
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forall (n_pre: Z) (s_pre: Z) (d_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (l': (@list Z)) (d: Z) (s: Z) (l: (@list Z)) (n: Z) (i: Z) ,
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[| (i >= n) |]
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&& [| (0 <= i) |]
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&& [| (i <= n) |]
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&& [| ((Zlength (l)) = n) |]
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&& [| (list_store_Z l val ) |]
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&& [| (n <= cap1) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l_2)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l_2 val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array s n l )
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** (store_undef_uint_array_rec s n cap1 )
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** (store_uint_array d i (sublist (0) (i) (l)) )
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** (store_uint_array_rec d i cap2 l' )
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|--
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(mpd_store_Z s_pre val n_pre cap1 )
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** (mpd_store_Z d_pre val n_pre cap2 )
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.
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Definition mpn_copyi_partial_solve_wit_1 :=
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forall (n_pre: Z) (s_pre: Z) (d_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) ,
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[| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (mpd_store_Z s_pre val n_pre cap1 )
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** (store_uint_array d_pre cap2 l2 )
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|--
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[| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (mpd_store_Z s_pre val n_pre cap1 )
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** (store_uint_array d_pre cap2 l2 )
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.
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Definition mpn_copyi_partial_solve_wit_2_pure :=
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forall (n_pre: Z) (s_pre: Z) (d_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) ,
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[| (n_pre <= cap1) |]
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&& [| ((Zlength (l)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& ((( &( "n" ) )) # Int |-> n_pre)
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** ((( &( "s" ) )) # Ptr |-> s_pre)
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** (store_uint_array s_pre n_pre l )
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** (store_undef_uint_array_rec s_pre n_pre cap1 )
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** ((( &( "d" ) )) # Ptr |-> d_pre)
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** (store_uint_array d_pre cap2 l2 )
|
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|--
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[| ((Zlength (l2)) = cap2) |]
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.
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Definition mpn_copyi_partial_solve_wit_2_aux :=
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forall (n_pre: Z) (s_pre: Z) (d_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) ,
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[| (n_pre <= cap1) |]
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&& [| ((Zlength (l)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array s_pre n_pre l )
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** (store_undef_uint_array_rec s_pre n_pre cap1 )
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** (store_uint_array d_pre cap2 l2 )
|
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|--
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[| ((Zlength (l2)) = cap2) |]
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&& [| (n_pre <= cap1) |]
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&& [| ((Zlength (l)) = n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (list_store_Z l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& (store_uint_array d_pre cap2 l2 )
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** (store_uint_array s_pre n_pre l )
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** (store_undef_uint_array_rec s_pre n_pre cap1 )
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.
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Definition mpn_copyi_partial_solve_wit_2 := mpn_copyi_partial_solve_wit_2_pure -> mpn_copyi_partial_solve_wit_2_aux.
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Definition mpn_copyi_partial_solve_wit_3_pure :=
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forall (n_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (l': (@list Z)) (d: Z) (s: Z) (l: (@list Z)) (n: Z) (i: Z) ,
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[| (i < n) |]
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&& [| (0 <= i) |]
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&& [| (i <= n) |]
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&& [| ((Zlength (l)) = n) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& [| (n <= cap1) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| ((Zlength (l_2)) = n_pre) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l_2 val ) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (cap2 >= n_pre) |]
|
|
&& ((( &( "i" ) )) # Int |-> i)
|
|
** ((( &( "n" ) )) # Int |-> n)
|
|
** ((( &( "s" ) )) # Ptr |-> s)
|
|
** (store_uint_array s n l )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
** ((( &( "d" ) )) # Ptr |-> d)
|
|
** (store_uint_array d i (sublist (0) (i) (l)) )
|
|
** (store_uint_array_rec d i cap2 l' )
|
|
|--
|
|
[| (0 <= i) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
.
|
|
|
|
Definition mpn_copyi_partial_solve_wit_3_aux :=
|
|
forall (n_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (l': (@list Z)) (d: Z) (s: Z) (l_2: (@list Z)) (n: Z) (i: Z) ,
|
|
[| (i < n) |]
|
|
&& [| (0 <= i) |]
|
|
&& [| (i <= n) |]
|
|
&& [| ((Zlength (l_2)) = n) |]
|
|
&& [| (list_store_Z l_2 val ) |]
|
|
&& [| (n <= cap1) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (cap2 >= n_pre) |]
|
|
&& (store_uint_array s n l_2 )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
** (store_uint_array d i (sublist (0) (i) (l_2)) )
|
|
** (store_uint_array_rec d i cap2 l' )
|
|
|--
|
|
[| (0 <= i) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
&& [| (i < n) |]
|
|
&& [| (0 <= i) |]
|
|
&& [| (i <= n) |]
|
|
&& [| ((Zlength (l_2)) = n) |]
|
|
&& [| (list_store_Z l_2 val ) |]
|
|
&& [| (n <= cap1) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (cap2 >= n_pre) |]
|
|
&& (store_uint_array_rec d i cap2 l' )
|
|
** (store_uint_array d i (sublist (0) (i) (l_2)) )
|
|
** (store_uint_array s n l_2 )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
.
|
|
|
|
Definition mpn_copyi_partial_solve_wit_3 := mpn_copyi_partial_solve_wit_3_pure -> mpn_copyi_partial_solve_wit_3_aux.
|
|
|
|
Definition mpn_copyi_partial_solve_wit_4 :=
|
|
forall (n_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (l': (@list Z)) (d: Z) (s: Z) (l_2: (@list Z)) (n: Z) (i: Z) (a: Z) (l2': (@list Z)) ,
|
|
[| (l' = (cons (a) (l2'))) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
&& [| (i < n) |]
|
|
&& [| (0 <= i) |]
|
|
&& [| (i <= n) |]
|
|
&& [| ((Zlength (l_2)) = n) |]
|
|
&& [| (list_store_Z l_2 val ) |]
|
|
&& [| (n <= cap1) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (cap2 >= n_pre) |]
|
|
&& (store_uint_array_rec d (i + 1 ) cap2 l2' )
|
|
** (store_uint_array d (i + 1 ) (app ((sublist (0) (i) (l_2))) ((cons (a) (nil)))) )
|
|
** (store_uint_array s n l_2 )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
|--
|
|
[| (l' = (cons (a) (l2'))) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
&& [| (i < n) |]
|
|
&& [| (0 <= i) |]
|
|
&& [| (i <= n) |]
|
|
&& [| ((Zlength (l_2)) = n) |]
|
|
&& [| (list_store_Z l_2 val ) |]
|
|
&& [| (n <= cap1) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (cap2 >= n_pre) |]
|
|
&& (((s + (i * sizeof(UINT) ) )) # UInt |-> (Znth i l_2 0))
|
|
** (store_uint_array_missing_i_rec s i 0 n l_2 )
|
|
** (store_uint_array_rec d (i + 1 ) cap2 l2' )
|
|
** (store_uint_array d (i + 1 ) (app ((sublist (0) (i) (l_2))) ((cons (a) (nil)))) )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
.
|
|
|
|
Definition mpn_copyi_partial_solve_wit_5 :=
|
|
forall (n_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (l': (@list Z)) (d: Z) (s: Z) (l_2: (@list Z)) (n: Z) (i: Z) (a: Z) (l2': (@list Z)) ,
|
|
[| (l' = (cons (a) (l2'))) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
&& [| (i < n) |]
|
|
&& [| (0 <= i) |]
|
|
&& [| (i <= n) |]
|
|
&& [| ((Zlength (l_2)) = n) |]
|
|
&& [| (list_store_Z l_2 val ) |]
|
|
&& [| (n <= cap1) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (cap2 >= n_pre) |]
|
|
&& (store_uint_array s n l_2 )
|
|
** (store_uint_array_rec d (i + 1 ) cap2 l2' )
|
|
** (store_uint_array d (i + 1 ) (app ((sublist (0) (i) (l_2))) ((cons (a) (nil)))) )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
|--
|
|
[| (l' = (cons (a) (l2'))) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
&& [| (i < n) |]
|
|
&& [| (0 <= i) |]
|
|
&& [| (i <= n) |]
|
|
&& [| ((Zlength (l_2)) = n) |]
|
|
&& [| (list_store_Z l_2 val ) |]
|
|
&& [| (n <= cap1) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& [| ((Zlength (l2)) = cap2) |]
|
|
&& [| (cap2 >= n_pre) |]
|
|
&& (((d + (i * sizeof(UINT) ) )) # UInt |->_)
|
|
** (store_uint_array_missing_i_rec d i 0 (i + 1 ) (app ((sublist (0) (i) (l_2))) ((cons (a) (nil)))) )
|
|
** (store_uint_array s n l_2 )
|
|
** (store_uint_array_rec d (i + 1 ) cap2 l2' )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
.
|
|
|
|
Definition mpn_copyi_which_implies_wit_1 :=
|
|
forall (cap1: Z) (val: Z) (n: Z) (s: Z) ,
|
|
(mpd_store_Z s val n cap1 )
|
|
|--
|
|
EX (l: (@list Z)) ,
|
|
[| (n <= cap1) |]
|
|
&& [| ((Zlength (l)) = n) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (list_store_Z l val ) |]
|
|
&& (store_uint_array s n l )
|
|
** (store_undef_uint_array_rec s n cap1 )
|
|
.
|
|
|
|
Definition mpn_copyi_which_implies_wit_2 :=
|
|
forall (cap2: Z) (l2: (@list Z)) (d: Z) ,
|
|
[| ((Zlength (l2)) = cap2) |]
|
|
&& (store_uint_array d cap2 l2 )
|
|
|--
|
|
[| ((Zlength (l2)) = cap2) |]
|
|
&& (store_uint_array_rec d 0 cap2 l2 )
|
|
** (store_uint_array d 0 nil )
|
|
.
|
|
|
|
Definition mpn_copyi_which_implies_wit_3 :=
|
|
forall (cap2: Z) (l': (@list Z)) (l: (@list Z)) (i: Z) (n: Z) (d: Z) ,
|
|
[| (0 <= i) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
&& (store_uint_array_rec d i cap2 l' )
|
|
** (store_uint_array d i (sublist (0) (i) (l)) )
|
|
|--
|
|
EX (a: Z) (l2': (@list Z)) ,
|
|
[| (l' = (cons (a) (l2'))) |]
|
|
&& [| (i < n) |]
|
|
&& [| (n <= cap2) |]
|
|
&& (store_uint_array_rec d (i + 1 ) cap2 l2' )
|
|
** (store_uint_array d (i + 1 ) (app ((sublist (0) (i) (l))) ((cons (a) (nil)))) )
|
|
.
|
|
|
|
(*----- Function mpn_cmp -----*)
|
|
|
|
Definition mpn_cmp_safety_wit_1 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) ,
|
|
[| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
** ((( &( "n" ) )) # Int |-> n_pre)
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
|--
|
|
[| ((n_pre - 1 ) <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= (n_pre - 1 )) |]
|
|
.
|
|
|
|
Definition mpn_cmp_safety_wit_2 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& ((( &( "n" ) )) # Int |-> n)
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpn_cmp_safety_wit_3 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((Znth n l1 0) <= (Znth n l2 0)) |]
|
|
&& [| ((Znth n l1 0) <> (Znth n l2 0)) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array bp_pre n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** ((( &( "n" ) )) # Int |-> n)
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
|--
|
|
[| (1 <> (INT_MIN)) |]
|
|
.
|
|
|
|
Definition mpn_cmp_safety_wit_4 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((Znth n l1 0) <= (Znth n l2 0)) |]
|
|
&& [| ((Znth n l1 0) <> (Znth n l2 0)) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array bp_pre n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** ((( &( "n" ) )) # Int |-> n)
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
|--
|
|
[| (1 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 1) |]
|
|
.
|
|
|
|
Definition mpn_cmp_safety_wit_5 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((Znth n l1 0) > (Znth n l2 0)) |]
|
|
&& [| ((Znth n l1 0) <> (Znth n l2 0)) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array bp_pre n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** ((( &( "n" ) )) # Int |-> n)
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
|--
|
|
[| (1 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 1) |]
|
|
.
|
|
|
|
Definition mpn_cmp_safety_wit_6 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((Znth n l1 0) = (Znth n l2 0)) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array bp_pre n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** ((( &( "n" ) )) # Int |-> n)
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
|--
|
|
[| ((n - 1 ) <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= (n - 1 )) |]
|
|
.
|
|
|
|
Definition mpn_cmp_safety_wit_7 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| (n < 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& ((( &( "n" ) )) # Int |-> n)
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpn_cmp_entail_wit_1 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) ,
|
|
[| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
|--
|
|
[| ((-1) <= (n_pre - 1 )) |]
|
|
&& [| ((n_pre - 1 ) < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist (((n_pre - 1 ) + 1 )) (n_pre) (l1)) = (sublist (((n_pre - 1 ) + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
.
|
|
|
|
Definition mpn_cmp_entail_wit_2 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((Znth n l1 0) = (Znth n l2 0)) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array bp_pre n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
|--
|
|
[| ((-1) <= (n - 1 )) |]
|
|
&& [| ((n - 1 ) < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist (((n - 1 ) + 1 )) (n_pre) (l1)) = (sublist (((n - 1 ) + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
.
|
|
|
|
Definition mpn_cmp_return_wit_1_1 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((Znth n l1 0) <= (Znth n l2 0)) |]
|
|
&& [| ((Znth n l1 0) <> (Znth n l2 0)) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array bp_pre n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| ((-1) = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| ((-1) = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| ((-1) = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp_return_wit_1_2 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| ((Znth n l1 0) > (Znth n l2 0)) |]
|
|
&& [| ((Znth n l1 0) <> (Znth n l2 0)) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array bp_pre n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| (1 = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| (1 = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| (1 = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp_return_wit_2 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| (n < 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| (0 = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| (0 = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| (0 = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp_partial_solve_wit_1 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 )
|
|
|--
|
|
[| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 )
|
|
.
|
|
|
|
Definition mpn_cmp_partial_solve_wit_2 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
|--
|
|
[| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (((ap_pre + (n * sizeof(UINT) ) )) # UInt |-> (Znth n l1 0))
|
|
** (store_uint_array_missing_i_rec ap_pre n 0 n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
.
|
|
|
|
Definition mpn_cmp_partial_solve_wit_3 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (l1: (@list Z)) (n: Z) ,
|
|
[| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
|--
|
|
[| (n >= 0) |]
|
|
&& [| ((-1) <= n) |]
|
|
&& [| (n < n_pre) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| ((sublist ((n + 1 )) (n_pre) (l1)) = (sublist ((n + 1 )) (n_pre) (l2))) |]
|
|
&& [| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap1) |]
|
|
&& [| (n_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (((bp_pre + (n * sizeof(UINT) ) )) # UInt |-> (Znth n l2 0))
|
|
** (store_uint_array_missing_i_rec bp_pre n 0 n_pre l2 )
|
|
** (store_uint_array ap_pre n_pre l1 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
.
|
|
|
|
Definition mpn_cmp_which_implies_wit_1 :=
|
|
forall (n_pre: Z) (bp_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
(mpd_store_Z_compact ap_pre val1 n_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 n_pre cap2 )
|
|
|--
|
|
EX (l2: (@list Z)) (l1: (@list Z)) ,
|
|
[| (list_store_Z_compact l1 val1 ) |]
|
|
&& [| (list_store_Z_compact l2 val2 ) |]
|
|
&& [| (n_pre = (Zlength (l1))) |]
|
|
&& [| (n_pre = (Zlength (l2))) |]
|
|
&& (store_uint_array ap_pre n_pre l1 )
|
|
** (store_uint_array bp_pre n_pre l2 )
|
|
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
|
** (store_undef_uint_array_rec bp_pre n_pre cap2 )
|
|
.
|
|
|
|
(*----- Function mpn_cmp4 -----*)
|
|
|
|
Definition mpn_cmp4_safety_wit_1 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre >= bn_pre) |]
|
|
&& [| (an_pre <> bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& ((( &( "bn" ) )) # Int |-> bn_pre)
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "an" ) )) # Int |-> an_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
** (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
[| (1 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 1) |]
|
|
.
|
|
|
|
Definition mpn_cmp4_safety_wit_2 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre < bn_pre) |]
|
|
&& [| (an_pre <> bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& ((( &( "bn" ) )) # Int |-> bn_pre)
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "an" ) )) # Int |-> an_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
** (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
[| (1 <> (INT_MIN)) |]
|
|
.
|
|
|
|
Definition mpn_cmp4_safety_wit_3 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre < bn_pre) |]
|
|
&& [| (an_pre <> bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& ((( &( "bn" ) )) # Int |-> bn_pre)
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "an" ) )) # Int |-> an_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
** (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
[| (1 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 1) |]
|
|
.
|
|
|
|
Definition mpn_cmp4_return_wit_1_1 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre >= bn_pre) |]
|
|
&& [| (an_pre <> bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| (1 = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| (1 = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| (1 = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp4_return_wit_1_2 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre < bn_pre) |]
|
|
&& [| (an_pre <> bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| ((-1) = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| ((-1) = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| ((-1) = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp4_return_wit_2_1 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (retval: Z) ,
|
|
[| (val1 > val2) |]
|
|
&& [| (retval = 1) |]
|
|
&& [| (an_pre <= cap2) |]
|
|
&& [| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 an_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| (retval = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| (retval = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| (retval = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp4_return_wit_2_2 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (retval: Z) ,
|
|
[| (val1 = val2) |]
|
|
&& [| (retval = 0) |]
|
|
&& [| (an_pre <= cap2) |]
|
|
&& [| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 an_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| (retval = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| (retval = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| (retval = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp4_return_wit_2_3 :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) (retval: Z) ,
|
|
[| (val1 < val2) |]
|
|
&& [| (retval = (-1)) |]
|
|
&& [| (an_pre <= cap2) |]
|
|
&& [| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 an_pre cap2 )
|
|
|--
|
|
([| (val1 < val2) |]
|
|
&& [| (retval = (-1)) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 = val2) |]
|
|
&& [| (retval = 0) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
||
|
|
([| (val1 > val2) |]
|
|
&& [| (retval = 1) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 ))
|
|
.
|
|
|
|
Definition mpn_cmp4_partial_solve_wit_1_pure :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& ((( &( "bn" ) )) # Int |-> bn_pre)
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "an" ) )) # Int |-> an_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
** (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
[| (an_pre = bn_pre) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
.
|
|
|
|
Definition mpn_cmp4_partial_solve_wit_1_aux :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
[| (an_pre = bn_pre) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
.
|
|
|
|
Definition mpn_cmp4_partial_solve_wit_1 := mpn_cmp4_partial_solve_wit_1_pure -> mpn_cmp4_partial_solve_wit_1_aux.
|
|
|
|
Definition mpn_cmp4_partial_solve_wit_2_pure :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre <= cap2) |]
|
|
&& [| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& ((( &( "bn" ) )) # Int |-> bn_pre)
|
|
** ((( &( "bp" ) )) # Ptr |-> bp_pre)
|
|
** ((( &( "an" ) )) # Int |-> an_pre)
|
|
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
|
|
** (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
[| (0 <= an_pre) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (an_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
.
|
|
|
|
Definition mpn_cmp4_partial_solve_wit_2_aux :=
|
|
forall (bn_pre: Z) (bp_pre: Z) (an_pre: Z) (ap_pre: Z) (val2: Z) (val1: Z) (cap2: Z) (cap1: Z) ,
|
|
[| (an_pre <= cap2) |]
|
|
&& [| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 bn_pre cap2 )
|
|
|--
|
|
[| (0 <= an_pre) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (an_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& [| (an_pre <= cap2) |]
|
|
&& [| (an_pre = bn_pre) |]
|
|
&& [| (an_pre >= 0) |]
|
|
&& [| (bn_pre >= 0) |]
|
|
&& [| (an_pre <= cap1) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& [| (cap1 <= 100000000) |]
|
|
&& [| (cap2 <= 100000000) |]
|
|
&& (mpd_store_Z_compact ap_pre val1 an_pre cap1 )
|
|
** (mpd_store_Z_compact bp_pre val2 an_pre cap2 )
|
|
.
|
|
|
|
Definition mpn_cmp4_partial_solve_wit_2 := mpn_cmp4_partial_solve_wit_2_pure -> mpn_cmp4_partial_solve_wit_2_aux.
|
|
|
|
Definition mpn_cmp4_which_implies_wit_1 :=
|
|
forall (bn_pre: Z) (an_pre: Z) (cap2: Z) ,
|
|
[| (an_pre = bn_pre) |]
|
|
&& [| (bn_pre <= cap2) |]
|
|
&& emp
|
|
|--
|
|
[| (an_pre <= cap2) |]
|
|
&& emp
|
|
.
|
|
|
|
(*----- Function mpn_normalized_size -----*)
|
|
|
|
Definition mpn_normalized_size_safety_wit_1 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& ((( &( "n" ) )) # Int |-> n)
|
|
** (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
** ((( &( "xp" ) )) # Ptr |-> xp_pre)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpn_normalized_size_safety_wit_2 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& ((( &( "n" ) )) # Int |-> n)
|
|
** (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
** ((( &( "xp" ) )) # Ptr |-> xp_pre)
|
|
|--
|
|
[| ((n - 1 ) <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= (n - 1 )) |]
|
|
.
|
|
|
|
Definition mpn_normalized_size_safety_wit_3 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& ((( &( "n" ) )) # Int |-> n)
|
|
** (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
** ((( &( "xp" ) )) # Ptr |-> xp_pre)
|
|
|--
|
|
[| (1 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 1) |]
|
|
.
|
|
|
|
Definition mpn_normalized_size_safety_wit_4 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** ((( &( "n" ) )) # Int |-> n)
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
** ((( &( "xp" ) )) # Ptr |-> xp_pre)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpn_normalized_size_safety_wit_5 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| ((Znth (n - 1 ) (sublist (0) (n) (l)) 0) = 0) |]
|
|
&& [| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** ((( &( "n" ) )) # Int |-> n)
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
** ((( &( "xp" ) )) # Ptr |-> xp_pre)
|
|
|--
|
|
[| ((n - 1 ) <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= (n - 1 )) |]
|
|
.
|
|
|
|
Definition mpn_normalized_size_entail_wit_1 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) ,
|
|
[| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n_pre (sublist (0) (n_pre) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n_pre cap )
|
|
|--
|
|
[| (n_pre >= 0) |]
|
|
&& [| (n_pre <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n_pre (sublist (0) (n_pre) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n_pre cap )
|
|
.
|
|
|
|
Definition mpn_normalized_size_entail_wit_2 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| ((Znth (n - 1 ) (sublist (0) (n) (l)) 0) = 0) |]
|
|
&& [| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
|--
|
|
[| ((n - 1 ) >= 0) |]
|
|
&& [| ((n - 1 ) <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) ((n - 1 )) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre (n - 1 ) (sublist (0) ((n - 1 )) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre (n - 1 ) cap )
|
|
.
|
|
|
|
Definition mpn_normalized_size_return_wit_1_1 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| (n <= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
|--
|
|
[| (0 <= n) |]
|
|
&& [| (n <= cap) |]
|
|
&& (mpd_store_Z_compact xp_pre val n cap )
|
|
.
|
|
|
|
Definition mpn_normalized_size_return_wit_1_2 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| ((Znth (n - 1 ) (sublist (0) (n) (l)) 0) <> 0) |]
|
|
&& [| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
|--
|
|
[| (0 <= n) |]
|
|
&& [| (n <= cap) |]
|
|
&& (mpd_store_Z_compact xp_pre val n cap )
|
|
.
|
|
|
|
Definition mpn_normalized_size_partial_solve_wit_1 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) ,
|
|
[| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (mpd_store_Z xp_pre val n_pre cap )
|
|
|--
|
|
[| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (mpd_store_Z xp_pre val n_pre cap )
|
|
.
|
|
|
|
Definition mpn_normalized_size_partial_solve_wit_2 :=
|
|
forall (n_pre: Z) (xp_pre: Z) (val: Z) (cap: Z) (l: (@list Z)) (n: Z) ,
|
|
[| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
|--
|
|
[| (n > 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& [| (n <= n_pre) |]
|
|
&& [| (n_pre >= 0) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| (list_store_Z (sublist (0) (n_pre) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n_pre) |]
|
|
&& [| (0 <= n_pre) |]
|
|
&& [| (n_pre <= cap) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& (((xp_pre + ((n - 1 ) * sizeof(UINT) ) )) # UInt |-> (Znth (n - 1 ) (sublist (0) (n) (l)) 0))
|
|
** (store_uint_array_missing_i_rec xp_pre (n - 1 ) 0 n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
.
|
|
|
|
Definition mpn_normalized_size_which_implies_wit_1 :=
|
|
forall (xp_pre: Z) (val: Z) (cap: Z) (n: Z) ,
|
|
(mpd_store_Z xp_pre val n cap )
|
|
|--
|
|
EX (l: (@list Z)) ,
|
|
[| (list_store_Z (sublist (0) (n) (l)) val ) |]
|
|
&& [| ((Zlength (l)) = n) |]
|
|
&& (store_uint_array xp_pre n (sublist (0) (n) (l)) )
|
|
** (store_undef_uint_array_rec xp_pre n cap )
|
|
.
|
|
|
|
(*----- Function mpz_clear -----*)
|
|
|
|
Definition mpz_clear_return_wit_1_1 :=
|
|
forall (r_pre: Z) (n: Z) (ptr_2: Z) (cap_2: Z) (size_2: Z) ,
|
|
[| (cap_2 = 0) |]
|
|
&& [| (size_2 < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_2 (-n) (-size_2) cap_2 )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_2)
|
|
|--
|
|
EX (ptr: Z) (cap: Z) (size: Z) ,
|
|
((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_clear_return_wit_1_2 :=
|
|
forall (r_pre: Z) (n: Z) (ptr_2: Z) (cap_2: Z) (size_2: Z) ,
|
|
[| (cap_2 = 0) |]
|
|
&& [| (size_2 >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_2 n size_2 cap_2 )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_2)
|
|
|--
|
|
EX (ptr: Z) (cap: Z) (size: Z) ,
|
|
((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_clear_return_wit_1_3 :=
|
|
forall (r_pre: Z) (n: Z) (ptr_2: Z) (cap_2: Z) (size_2: Z) ,
|
|
[| (cap_2 <> 0) |]
|
|
&& [| (size_2 >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_2)
|
|
|--
|
|
EX (ptr: Z) (cap: Z) (size: Z) ,
|
|
((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_clear_return_wit_1_4 :=
|
|
forall (r_pre: Z) (n: Z) (ptr_2: Z) (cap_2: Z) (size_2: Z) ,
|
|
[| (cap_2 <> 0) |]
|
|
&& [| (size_2 < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_2)
|
|
|--
|
|
EX (ptr: Z) (cap: Z) (size: Z) ,
|
|
((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_clear_partial_solve_wit_1 :=
|
|
forall (r_pre: Z) (n: Z) ,
|
|
(store_Z r_pre n )
|
|
|--
|
|
(store_Z r_pre n )
|
|
.
|
|
|
|
Definition mpz_clear_partial_solve_wit_2 :=
|
|
forall (r_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (size >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n size cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (cap <> 0) |]
|
|
&& [| (size >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n size cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_clear_partial_solve_wit_3 :=
|
|
forall (r_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (size < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (cap <> 0) |]
|
|
&& [| (size < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_clear_which_implies_wit_1 :=
|
|
forall (r_pre: Z) (n: Z) ,
|
|
(store_Z r_pre n )
|
|
|--
|
|
(EX (ptr: Z) (cap: Z) (size: Z) ,
|
|
[| (size >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n size cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr))
|
|
||
|
|
(EX (ptr: Z) (cap: Z) (size: Z) ,
|
|
[| (size < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr))
|
|
.
|
|
|
|
(*----- Function mpz_realloc -----*)
|
|
|
|
Definition mpz_realloc_safety_wit_1 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) ,
|
|
[| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& ((( &( "size" ) )) # Int |-> size_pre)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (1 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 1) |]
|
|
.
|
|
|
|
Definition mpz_realloc_safety_wit_2 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) ,
|
|
[| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& ((( &( "size" ) )) # Int |-> size_pre)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (1 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 1) |]
|
|
.
|
|
|
|
Definition mpz_realloc_safety_wit_3 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (store_undef_uint_array retval_3 retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpz_realloc_safety_wit_4 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (store_undef_uint_array retval_3 retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpz_realloc_safety_wit_5 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact retval_3 (-n) (-old) retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpz_realloc_safety_wit_6 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact retval_3 n old retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
[| (0 <= INT_MAX) |]
|
|
&& [| ((INT_MIN) <= 0) |]
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_1 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval <= retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact retval_3 n old retval_2 )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_2 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval <= retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact retval_3 (-n) (-old) retval_2 )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_3 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval <= retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (store_undef_uint_array retval_3 retval_2 )
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_4 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval <= retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (store_undef_uint_array retval_3 retval_2 )
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_5 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (store_undef_uint_array retval_3 retval_2 )
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> 0)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_6 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (store_undef_uint_array retval_3 retval_2 )
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> 0)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_7 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact retval_3 (-n) (-old) retval_2 )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> 0)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_return_wit_1_8 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3: Z) (retval: Z) ,
|
|
[| (retval > retval_2) |]
|
|
&& [| (retval = (Zabs (old))) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact retval_3 n old retval_2 )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> 0)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_3)
|
|
|--
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr_new (-n) (-old) c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
||
|
|
(EX (ptr_new: Z) (c: Z) ,
|
|
[| (c >= size_pre) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr_new n old c )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> c)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr_new))
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_1 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) ,
|
|
[| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_2 :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) ,
|
|
[| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_3_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& ((( &( "size" ) )) # Int |-> retval)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (cap >= 0) |]
|
|
&& [| (retval >= cap) |]
|
|
&& [| ((Zmax (size_pre) (1)) >= cap) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_3_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (cap >= 0) |]
|
|
&& [| (retval >= cap) |]
|
|
&& [| ((Zmax (size_pre) (1)) >= cap) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_3 := mpz_realloc_partial_solve_wit_3_pure -> mpz_realloc_partial_solve_wit_3_aux.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_4_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& ((( &( "size" ) )) # Int |-> retval)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (cap >= 0) |]
|
|
&& [| (retval >= cap) |]
|
|
&& [| ((Zmax (size_pre) (1)) >= cap) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_4_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (cap >= 0) |]
|
|
&& [| (retval >= cap) |]
|
|
&& [| ((Zmax (size_pre) (1)) >= cap) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_4 := mpz_realloc_partial_solve_wit_4_pure -> mpz_realloc_partial_solve_wit_4_aux.
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|
|
Definition mpz_realloc_partial_solve_wit_5_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& ((( &( "size" ) )) # Int |-> retval)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (retval >= 0) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_5_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (retval >= 0) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_5 := mpz_realloc_partial_solve_wit_5_pure -> mpz_realloc_partial_solve_wit_5_aux.
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|
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Definition mpz_realloc_partial_solve_wit_6_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& ((( &( "size" ) )) # Int |-> retval)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (retval >= 0) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_6_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
|--
|
|
[| (retval >= 0) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_6 := mpz_realloc_partial_solve_wit_6_pure -> mpz_realloc_partial_solve_wit_6_aux.
|
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|
|
Definition mpz_realloc_partial_solve_wit_7_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (store_undef_uint_array retval retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval)
|
|
|--
|
|
[| (old <= INT_MAX) |]
|
|
&& [| (INT_MIN < old) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_7_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) (retval_2: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (store_undef_uint_array retval_2 retval )
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
|--
|
|
[| (old <= INT_MAX) |]
|
|
&& [| (INT_MIN < old) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (store_undef_uint_array retval_2 retval )
|
|
** (mpd_store_Z_compact ptr (-n) (-old) cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_7 := mpz_realloc_partial_solve_wit_7_pure -> mpz_realloc_partial_solve_wit_7_aux.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_8_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (store_undef_uint_array retval retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval)
|
|
|--
|
|
[| (INT_MIN < old) |]
|
|
&& [| (old <= INT_MAX) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_8_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) (retval_2: Z) ,
|
|
[| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (store_undef_uint_array retval_2 retval )
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
|--
|
|
[| (INT_MIN < old) |]
|
|
&& [| (old <= INT_MAX) |]
|
|
&& [| (cap = 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (store_undef_uint_array retval_2 retval )
|
|
** (mpd_store_Z_compact ptr n old cap )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_8 := mpz_realloc_partial_solve_wit_8_pure -> mpz_realloc_partial_solve_wit_8_aux.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_9_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact retval (-n) (-old) retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval)
|
|
|--
|
|
[| (old <= INT_MAX) |]
|
|
&& [| (INT_MIN < old) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_9_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval: Z) (retval_2: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact retval_2 (-n) (-old) retval )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
|--
|
|
[| (old <= INT_MAX) |]
|
|
&& [| (INT_MIN < old) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old < 0) |]
|
|
&& [| (n < 0) |]
|
|
&& (mpd_store_Z_compact retval_2 (-n) (-old) retval )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_9 := mpz_realloc_partial_solve_wit_9_pure -> mpz_realloc_partial_solve_wit_9_aux.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_10_pure :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact retval n old retval_2 )
|
|
** ((( &( "size" ) )) # Int |-> retval_2)
|
|
** ((( &( "r" ) )) # Ptr |-> r_pre)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval_2)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval)
|
|
|--
|
|
[| (INT_MIN < old) |]
|
|
&& [| (old <= INT_MAX) |]
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_10_aux :=
|
|
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval: Z) (retval_2: Z) ,
|
|
[| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact retval_2 n old retval )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
|--
|
|
[| (INT_MIN < old) |]
|
|
&& [| (old <= INT_MAX) |]
|
|
&& [| (cap <> 0) |]
|
|
&& [| (retval = (Zmax (size_pre) (1))) |]
|
|
&& [| (size_pre >= cap) |]
|
|
&& [| (size_pre <= 100000000) |]
|
|
&& [| (cap >= 0) |]
|
|
&& [| (cap <= 100000000) |]
|
|
&& [| (old >= 0) |]
|
|
&& [| (n >= 0) |]
|
|
&& (mpd_store_Z_compact retval_2 n old retval )
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> old)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> retval)
|
|
** ((&((r_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> retval_2)
|
|
.
|
|
|
|
Definition mpz_realloc_partial_solve_wit_10 := mpz_realloc_partial_solve_wit_10_pure -> mpz_realloc_partial_solve_wit_10_aux.
|
|
|
|
Module Type VC_Correct.
|
|
|
|
Axiom proof_of_gmp_abs_safety_wit_1 : gmp_abs_safety_wit_1.
|
|
Axiom proof_of_gmp_abs_return_wit_1_1 : gmp_abs_return_wit_1_1.
|
|
Axiom proof_of_gmp_abs_return_wit_1_2 : gmp_abs_return_wit_1_2.
|
|
Axiom proof_of_gmp_max_return_wit_1_1 : gmp_max_return_wit_1_1.
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Axiom proof_of_gmp_max_return_wit_1_2 : gmp_max_return_wit_1_2.
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Axiom proof_of_gmp_cmp_safety_wit_1 : gmp_cmp_safety_wit_1.
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Axiom proof_of_gmp_cmp_safety_wit_2 : gmp_cmp_safety_wit_2.
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Axiom proof_of_gmp_cmp_safety_wit_3 : gmp_cmp_safety_wit_3.
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Axiom proof_of_gmp_cmp_safety_wit_4 : gmp_cmp_safety_wit_4.
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Axiom proof_of_gmp_cmp_return_wit_1_1 : gmp_cmp_return_wit_1_1.
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Axiom proof_of_gmp_cmp_return_wit_1_2 : gmp_cmp_return_wit_1_2.
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Axiom proof_of_gmp_cmp_return_wit_1_3 : gmp_cmp_return_wit_1_3.
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Axiom proof_of_mpn_copyi_safety_wit_1 : mpn_copyi_safety_wit_1.
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Axiom proof_of_mpn_copyi_safety_wit_2 : mpn_copyi_safety_wit_2.
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Axiom proof_of_mpn_copyi_entail_wit_1 : mpn_copyi_entail_wit_1.
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Axiom proof_of_mpn_copyi_entail_wit_2 : mpn_copyi_entail_wit_2.
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Axiom proof_of_mpn_copyi_return_wit_1 : mpn_copyi_return_wit_1.
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Axiom proof_of_mpn_copyi_partial_solve_wit_1 : mpn_copyi_partial_solve_wit_1.
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Axiom proof_of_mpn_copyi_partial_solve_wit_2_pure : mpn_copyi_partial_solve_wit_2_pure.
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Axiom proof_of_mpn_copyi_partial_solve_wit_2 : mpn_copyi_partial_solve_wit_2.
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Axiom proof_of_mpn_copyi_partial_solve_wit_3_pure : mpn_copyi_partial_solve_wit_3_pure.
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Axiom proof_of_mpn_copyi_partial_solve_wit_3 : mpn_copyi_partial_solve_wit_3.
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Axiom proof_of_mpn_copyi_partial_solve_wit_4 : mpn_copyi_partial_solve_wit_4.
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Axiom proof_of_mpn_copyi_partial_solve_wit_5 : mpn_copyi_partial_solve_wit_5.
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Axiom proof_of_mpn_copyi_which_implies_wit_1 : mpn_copyi_which_implies_wit_1.
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Axiom proof_of_mpn_copyi_which_implies_wit_2 : mpn_copyi_which_implies_wit_2.
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Axiom proof_of_mpn_copyi_which_implies_wit_3 : mpn_copyi_which_implies_wit_3.
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Axiom proof_of_mpn_cmp_safety_wit_1 : mpn_cmp_safety_wit_1.
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Axiom proof_of_mpn_cmp_safety_wit_2 : mpn_cmp_safety_wit_2.
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Axiom proof_of_mpn_cmp_safety_wit_3 : mpn_cmp_safety_wit_3.
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Axiom proof_of_mpn_cmp_safety_wit_4 : mpn_cmp_safety_wit_4.
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Axiom proof_of_mpn_cmp_safety_wit_5 : mpn_cmp_safety_wit_5.
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Axiom proof_of_mpn_cmp_safety_wit_6 : mpn_cmp_safety_wit_6.
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Axiom proof_of_mpn_cmp_safety_wit_7 : mpn_cmp_safety_wit_7.
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Axiom proof_of_mpn_cmp_entail_wit_1 : mpn_cmp_entail_wit_1.
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Axiom proof_of_mpn_cmp_entail_wit_2 : mpn_cmp_entail_wit_2.
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Axiom proof_of_mpn_cmp_return_wit_1_1 : mpn_cmp_return_wit_1_1.
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Axiom proof_of_mpn_cmp_return_wit_1_2 : mpn_cmp_return_wit_1_2.
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Axiom proof_of_mpn_cmp_return_wit_2 : mpn_cmp_return_wit_2.
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Axiom proof_of_mpn_cmp_partial_solve_wit_1 : mpn_cmp_partial_solve_wit_1.
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Axiom proof_of_mpn_cmp_partial_solve_wit_2 : mpn_cmp_partial_solve_wit_2.
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Axiom proof_of_mpn_cmp_partial_solve_wit_3 : mpn_cmp_partial_solve_wit_3.
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Axiom proof_of_mpn_cmp_which_implies_wit_1 : mpn_cmp_which_implies_wit_1.
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Axiom proof_of_mpn_cmp4_safety_wit_1 : mpn_cmp4_safety_wit_1.
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Axiom proof_of_mpn_cmp4_safety_wit_2 : mpn_cmp4_safety_wit_2.
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Axiom proof_of_mpn_cmp4_safety_wit_3 : mpn_cmp4_safety_wit_3.
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Axiom proof_of_mpn_cmp4_return_wit_1_1 : mpn_cmp4_return_wit_1_1.
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Axiom proof_of_mpn_cmp4_return_wit_1_2 : mpn_cmp4_return_wit_1_2.
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Axiom proof_of_mpn_cmp4_return_wit_2_1 : mpn_cmp4_return_wit_2_1.
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Axiom proof_of_mpn_cmp4_return_wit_2_2 : mpn_cmp4_return_wit_2_2.
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Axiom proof_of_mpn_cmp4_return_wit_2_3 : mpn_cmp4_return_wit_2_3.
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Axiom proof_of_mpn_cmp4_partial_solve_wit_1_pure : mpn_cmp4_partial_solve_wit_1_pure.
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Axiom proof_of_mpn_cmp4_partial_solve_wit_1 : mpn_cmp4_partial_solve_wit_1.
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Axiom proof_of_mpn_cmp4_partial_solve_wit_2_pure : mpn_cmp4_partial_solve_wit_2_pure.
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Axiom proof_of_mpn_cmp4_partial_solve_wit_2 : mpn_cmp4_partial_solve_wit_2.
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Axiom proof_of_mpn_cmp4_which_implies_wit_1 : mpn_cmp4_which_implies_wit_1.
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Axiom proof_of_mpn_normalized_size_safety_wit_1 : mpn_normalized_size_safety_wit_1.
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Axiom proof_of_mpn_normalized_size_safety_wit_2 : mpn_normalized_size_safety_wit_2.
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Axiom proof_of_mpn_normalized_size_safety_wit_3 : mpn_normalized_size_safety_wit_3.
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Axiom proof_of_mpn_normalized_size_safety_wit_4 : mpn_normalized_size_safety_wit_4.
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Axiom proof_of_mpn_normalized_size_safety_wit_5 : mpn_normalized_size_safety_wit_5.
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Axiom proof_of_mpn_normalized_size_entail_wit_1 : mpn_normalized_size_entail_wit_1.
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Axiom proof_of_mpn_normalized_size_entail_wit_2 : mpn_normalized_size_entail_wit_2.
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Axiom proof_of_mpn_normalized_size_return_wit_1_1 : mpn_normalized_size_return_wit_1_1.
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Axiom proof_of_mpn_normalized_size_return_wit_1_2 : mpn_normalized_size_return_wit_1_2.
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Axiom proof_of_mpn_normalized_size_partial_solve_wit_1 : mpn_normalized_size_partial_solve_wit_1.
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Axiom proof_of_mpn_normalized_size_partial_solve_wit_2 : mpn_normalized_size_partial_solve_wit_2.
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Axiom proof_of_mpn_normalized_size_which_implies_wit_1 : mpn_normalized_size_which_implies_wit_1.
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Axiom proof_of_mpz_clear_return_wit_1_1 : mpz_clear_return_wit_1_1.
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Axiom proof_of_mpz_clear_return_wit_1_2 : mpz_clear_return_wit_1_2.
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Axiom proof_of_mpz_clear_return_wit_1_3 : mpz_clear_return_wit_1_3.
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Axiom proof_of_mpz_clear_return_wit_1_4 : mpz_clear_return_wit_1_4.
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Axiom proof_of_mpz_clear_partial_solve_wit_1 : mpz_clear_partial_solve_wit_1.
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Axiom proof_of_mpz_clear_partial_solve_wit_2 : mpz_clear_partial_solve_wit_2.
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Axiom proof_of_mpz_clear_partial_solve_wit_3 : mpz_clear_partial_solve_wit_3.
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Axiom proof_of_mpz_clear_which_implies_wit_1 : mpz_clear_which_implies_wit_1.
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Axiom proof_of_mpz_realloc_safety_wit_1 : mpz_realloc_safety_wit_1.
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Axiom proof_of_mpz_realloc_safety_wit_2 : mpz_realloc_safety_wit_2.
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Axiom proof_of_mpz_realloc_safety_wit_3 : mpz_realloc_safety_wit_3.
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Axiom proof_of_mpz_realloc_safety_wit_4 : mpz_realloc_safety_wit_4.
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Axiom proof_of_mpz_realloc_safety_wit_5 : mpz_realloc_safety_wit_5.
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Axiom proof_of_mpz_realloc_safety_wit_6 : mpz_realloc_safety_wit_6.
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Axiom proof_of_mpz_realloc_return_wit_1_1 : mpz_realloc_return_wit_1_1.
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Axiom proof_of_mpz_realloc_return_wit_1_2 : mpz_realloc_return_wit_1_2.
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Axiom proof_of_mpz_realloc_return_wit_1_3 : mpz_realloc_return_wit_1_3.
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Axiom proof_of_mpz_realloc_return_wit_1_4 : mpz_realloc_return_wit_1_4.
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Axiom proof_of_mpz_realloc_return_wit_1_5 : mpz_realloc_return_wit_1_5.
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Axiom proof_of_mpz_realloc_return_wit_1_6 : mpz_realloc_return_wit_1_6.
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Axiom proof_of_mpz_realloc_return_wit_1_7 : mpz_realloc_return_wit_1_7.
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Axiom proof_of_mpz_realloc_return_wit_1_8 : mpz_realloc_return_wit_1_8.
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Axiom proof_of_mpz_realloc_partial_solve_wit_1 : mpz_realloc_partial_solve_wit_1.
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Axiom proof_of_mpz_realloc_partial_solve_wit_2 : mpz_realloc_partial_solve_wit_2.
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Axiom proof_of_mpz_realloc_partial_solve_wit_3_pure : mpz_realloc_partial_solve_wit_3_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_3 : mpz_realloc_partial_solve_wit_3.
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Axiom proof_of_mpz_realloc_partial_solve_wit_4_pure : mpz_realloc_partial_solve_wit_4_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_4 : mpz_realloc_partial_solve_wit_4.
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Axiom proof_of_mpz_realloc_partial_solve_wit_5_pure : mpz_realloc_partial_solve_wit_5_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_5 : mpz_realloc_partial_solve_wit_5.
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Axiom proof_of_mpz_realloc_partial_solve_wit_6_pure : mpz_realloc_partial_solve_wit_6_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_6 : mpz_realloc_partial_solve_wit_6.
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Axiom proof_of_mpz_realloc_partial_solve_wit_7_pure : mpz_realloc_partial_solve_wit_7_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_7 : mpz_realloc_partial_solve_wit_7.
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Axiom proof_of_mpz_realloc_partial_solve_wit_8_pure : mpz_realloc_partial_solve_wit_8_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_8 : mpz_realloc_partial_solve_wit_8.
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Axiom proof_of_mpz_realloc_partial_solve_wit_9_pure : mpz_realloc_partial_solve_wit_9_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_9 : mpz_realloc_partial_solve_wit_9.
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Axiom proof_of_mpz_realloc_partial_solve_wit_10_pure : mpz_realloc_partial_solve_wit_10_pure.
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Axiom proof_of_mpz_realloc_partial_solve_wit_10 : mpz_realloc_partial_solve_wit_10.
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End VC_Correct.
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