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feat(mpz_swap): Proved correctness of mpz_swap. Proved some previously admitted lemmas.

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xiaoh105
2025-06-22 21:00:50 +08:00
parent 77ccdd3e50
commit ff1fd68eb1
6 changed files with 795 additions and 20 deletions
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projects/lib/gmp_goal.v
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@ -6071,6 +6071,521 @@ forall (n: Z) (u: Z) ,
** ((&((u) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr))
.
(*----- Function mpz_swap -----*)
Definition mpz_swap_return_wit_1_1 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** (mpd_store_Z_compact ptr1 n size1 cap1 )
|--
(store_Z u_pre m )
** (store_Z v_pre n )
.
Definition mpz_swap_return_wit_1_2 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** (mpd_store_Z_compact ptr1 n size1 cap1 )
|--
(store_Z u_pre m )
** (store_Z v_pre n )
.
Definition mpz_swap_return_wit_1_3 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
|--
(store_Z u_pre m )
** (store_Z v_pre n )
.
Definition mpz_swap_return_wit_1_4 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
|--
(store_Z u_pre m )
** (store_Z v_pre n )
.
Definition mpz_swap_partial_solve_wit_1 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) ,
(store_Z u_pre n )
** (store_Z v_pre m )
|--
(store_Z u_pre n )
** (store_Z v_pre m )
.
Definition mpz_swap_partial_solve_wit_2 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) ,
[| (size1 < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** (store_Z v_pre m )
|--
[| (size1 < 0) |]
&& [| (n < 0) |]
&& (store_Z v_pre m )
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
.
Definition mpz_swap_partial_solve_wit_3 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) ,
[| (size1 >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** (store_Z v_pre m )
|--
[| (size1 >= 0) |]
&& [| (n >= 0) |]
&& (store_Z v_pre m )
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
.
Definition mpz_swap_partial_solve_wit_4 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
.
Definition mpz_swap_partial_solve_wit_5 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
.
Definition mpz_swap_partial_solve_wit_6 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
.
Definition mpz_swap_partial_solve_wit_7 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
.
Definition mpz_swap_partial_solve_wit_8 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
.
Definition mpz_swap_partial_solve_wit_9 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
.
Definition mpz_swap_partial_solve_wit_10 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
.
Definition mpz_swap_partial_solve_wit_11 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
|--
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
.
Definition mpz_swap_partial_solve_wit_12 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
|--
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** (mpd_store_Z_compact ptr1 n size1 cap1 )
.
Definition mpz_swap_partial_solve_wit_13 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
|--
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 >= 0) |]
&& [| (n >= 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** (mpd_store_Z_compact ptr1 n size1 cap1 )
.
Definition mpz_swap_partial_solve_wit_14 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
|--
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 m size2 cap2 )
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
.
Definition mpz_swap_partial_solve_wit_15 :=
forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
|--
[| (size2 < 0) |]
&& [| (m < 0) |]
&& [| (size1 < 0) |]
&& [| (n < 0) |]
&& ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
.
Definition mpz_swap_which_implies_wit_1 :=
forall (n: Z) (u: Z) ,
(store_Z u n )
|--
(EX (ptr1: Z) (cap1: Z) (size1: Z) ,
[| (size1 >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr1 n size1 cap1 )
** ((&((u) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1))
||
(EX (ptr1: Z) (cap1: Z) (size1: Z) ,
[| (size1 < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
** ((&((u) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size1)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap1)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr1))
.
Definition mpz_swap_which_implies_wit_2 :=
forall (m: Z) (v: Z) ,
(store_Z v m )
|--
(EX (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 >= 0) |]
&& [| (m >= 0) |]
&& (mpd_store_Z_compact ptr2 m size2 cap2 )
** ((&((v) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2))
||
(EX (ptr2: Z) (cap2: Z) (size2: Z) ,
[| (size2 < 0) |]
&& [| (m < 0) |]
&& (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
** ((&((v) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size2)
** ((&((v) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap2)
** ((&((v) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr2))
.
Module Type VC_Correct.
Axiom proof_of_gmp_abs_safety_wit_1 : gmp_abs_safety_wit_1.
@ -6249,5 +6764,26 @@ Axiom proof_of_mpz_sgn_partial_solve_wit_1 : mpz_sgn_partial_solve_wit_1.
Axiom proof_of_mpz_sgn_partial_solve_wit_2 : mpz_sgn_partial_solve_wit_2.
Axiom proof_of_mpz_sgn_partial_solve_wit_3 : mpz_sgn_partial_solve_wit_3.
Axiom proof_of_mpz_sgn_which_implies_wit_1 : mpz_sgn_which_implies_wit_1.
Axiom proof_of_mpz_swap_return_wit_1_1 : mpz_swap_return_wit_1_1.
Axiom proof_of_mpz_swap_return_wit_1_2 : mpz_swap_return_wit_1_2.
Axiom proof_of_mpz_swap_return_wit_1_3 : mpz_swap_return_wit_1_3.
Axiom proof_of_mpz_swap_return_wit_1_4 : mpz_swap_return_wit_1_4.
Axiom proof_of_mpz_swap_partial_solve_wit_1 : mpz_swap_partial_solve_wit_1.
Axiom proof_of_mpz_swap_partial_solve_wit_2 : mpz_swap_partial_solve_wit_2.
Axiom proof_of_mpz_swap_partial_solve_wit_3 : mpz_swap_partial_solve_wit_3.
Axiom proof_of_mpz_swap_partial_solve_wit_4 : mpz_swap_partial_solve_wit_4.
Axiom proof_of_mpz_swap_partial_solve_wit_5 : mpz_swap_partial_solve_wit_5.
Axiom proof_of_mpz_swap_partial_solve_wit_6 : mpz_swap_partial_solve_wit_6.
Axiom proof_of_mpz_swap_partial_solve_wit_7 : mpz_swap_partial_solve_wit_7.
Axiom proof_of_mpz_swap_partial_solve_wit_8 : mpz_swap_partial_solve_wit_8.
Axiom proof_of_mpz_swap_partial_solve_wit_9 : mpz_swap_partial_solve_wit_9.
Axiom proof_of_mpz_swap_partial_solve_wit_10 : mpz_swap_partial_solve_wit_10.
Axiom proof_of_mpz_swap_partial_solve_wit_11 : mpz_swap_partial_solve_wit_11.
Axiom proof_of_mpz_swap_partial_solve_wit_12 : mpz_swap_partial_solve_wit_12.
Axiom proof_of_mpz_swap_partial_solve_wit_13 : mpz_swap_partial_solve_wit_13.
Axiom proof_of_mpz_swap_partial_solve_wit_14 : mpz_swap_partial_solve_wit_14.
Axiom proof_of_mpz_swap_partial_solve_wit_15 : mpz_swap_partial_solve_wit_15.
Axiom proof_of_mpz_swap_which_implies_wit_1 : mpz_swap_which_implies_wit_1.
Axiom proof_of_mpz_swap_which_implies_wit_2 : mpz_swap_which_implies_wit_2.
End VC_Correct.