ready to finalize proof_of_mpn_add_1_entail_wit_2_1
This commit is contained in:
@ -1781,8 +1781,12 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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.
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Definition mpn_add_1_safety_wit_2 :=
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
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[| (l'' = (cons (a) (l'''))) |]
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&& [| (0 <= i) |]
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&& [| (i < n_pre) |]
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&& [| (n_pre <= cap2) |]
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&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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@ -1803,12 +1807,12 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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&& [| (cap2 <= 100000000) |]
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (store_uint_array_rec rp_pre i cap2 (replace_Znth ((i - i )) ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32))) (l'')) )
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&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32))) ((app (l') ((cons (a) (nil)))))) )
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** ((( &( "i" ) )) # Int |-> i)
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** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
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** (store_uint_array ap_pre n_pre l_2 )
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** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
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** ((( &( "i" ) )) # Int |-> i)
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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** (store_uint_array rp_pre i l' )
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** ((( &( "b" ) )) # UInt |-> 0)
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** ((( &( "n" ) )) # Int |-> n_pre)
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** ((( &( "ap" ) )) # Ptr |-> ap_pre)
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@ -1819,8 +1823,12 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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.
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Definition mpn_add_1_safety_wit_3 :=
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
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[| (l'' = (cons (a) (l'''))) |]
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&& [| (0 <= i) |]
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&& [| (i < n_pre) |]
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&& [| (n_pre <= cap2) |]
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&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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@ -1841,12 +1849,12 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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&& [| (cap2 <= 100000000) |]
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (store_uint_array_rec rp_pre i cap2 (replace_Znth ((i - i )) ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32))) (l'')) )
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&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32))) ((app (l') ((cons (a) (nil)))))) )
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** ((( &( "i" ) )) # Int |-> i)
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** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
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** (store_uint_array ap_pre n_pre l_2 )
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** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
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** ((( &( "i" ) )) # Int |-> i)
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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** (store_uint_array rp_pre i l' )
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** ((( &( "b" ) )) # UInt |-> 1)
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** ((( &( "n" ) )) # Int |-> n_pre)
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** ((( &( "ap" ) )) # Ptr |-> ap_pre)
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@ -1901,8 +1909,12 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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.
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Definition mpn_add_1_entail_wit_2_1 :=
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (b: Z) (l''_2: (@list Z)) (l'_2: (@list Z)) (val2_2: Z) (val1_2: Z) (l_3: (@list Z)) (i: Z) ,
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[| ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32)) < b) |]
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (b: Z) (l''_2: (@list Z)) (l'_2: (@list Z)) (val2_2: Z) (val1_2: Z) (l_3: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
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[| (l''_2 = (cons (a) (l'''))) |]
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&& [| (0 <= i) |]
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&& [| (i < n_pre) |]
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&& [| (n_pre <= cap2) |]
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&& [| ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32)) < b) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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@ -1923,10 +1935,10 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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&& [| (cap2 <= 100000000) |]
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (store_uint_array_rec rp_pre i cap2 (replace_Znth ((i - i )) ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32))) (l''_2)) )
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&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32))) ((app (l'_2) ((cons (a) (nil)))))) )
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** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
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** (store_uint_array ap_pre n_pre l_3 )
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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** (store_uint_array rp_pre i l'_2 )
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|--
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EX (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l: (@list Z)) ,
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[| (0 <= (i + 1 )) |]
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@ -1955,8 +1967,12 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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.
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Definition mpn_add_1_entail_wit_2_2 :=
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (b: Z) (l''_2: (@list Z)) (l'_2: (@list Z)) (val2_2: Z) (val1_2: Z) (l_3: (@list Z)) (i: Z) ,
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[| ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32)) >= b) |]
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (b: Z) (l''_2: (@list Z)) (l'_2: (@list Z)) (val2_2: Z) (val1_2: Z) (l_3: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
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[| (l''_2 = (cons (a) (l'''))) |]
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&& [| (0 <= i) |]
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&& [| (i < n_pre) |]
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&& [| (n_pre <= cap2) |]
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&& [| ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32)) >= b) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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@ -1977,10 +1993,10 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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&& [| (cap2 <= 100000000) |]
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (store_uint_array_rec rp_pre i cap2 (replace_Znth ((i - i )) ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32))) (l''_2)) )
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&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32))) ((app (l'_2) ((cons (a) (nil)))))) )
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** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
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** (store_uint_array ap_pre n_pre l_3 )
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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** (store_uint_array rp_pre i l'_2 )
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|--
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EX (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l: (@list Z)) ,
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[| (0 <= (i + 1 )) |]
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@ -2174,9 +2190,9 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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** (store_uint_array_rec rp_pre i cap2 l'' )
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.
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Definition mpn_add_1_partial_solve_wit_4 :=
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Definition mpn_add_1_partial_solve_wit_4_pure :=
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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@ -2198,39 +2214,22 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (store_uint_array ap_pre n_pre l_2 )
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** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
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** ((( &( "i" ) )) # Int |-> i)
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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** (store_uint_array rp_pre i l' )
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** (store_uint_array_rec rp_pre i cap2 l'' )
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** ((( &( "b" ) )) # UInt |-> 0)
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** ((( &( "n" ) )) # Int |-> n_pre)
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** ((( &( "ap" ) )) # Ptr |-> ap_pre)
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** ((( &( "rp" ) )) # Ptr |-> rp_pre)
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|--
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
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[| (0 <= i) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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&& [| (list_store_Z_compact l_2 val ) |]
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&& [| (n_pre <= cap1) |]
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&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
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&& [| (list_store_Z l' val2 ) |]
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&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
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&& [| ((Zlength (l')) = i) |]
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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_compact l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (cap2 <= 100000000) |]
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (((rp_pre + (i * sizeof(UINT) ) )) # UInt |->_)
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** (store_uint_array_missing_i_rec rp_pre i i cap2 l'' )
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** (store_uint_array ap_pre n_pre l_2 )
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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** (store_uint_array rp_pre i l' )
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&& [| (n_pre <= cap2) |]
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.
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Definition mpn_add_1_partial_solve_wit_5 :=
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Definition mpn_add_1_partial_solve_wit_4_aux :=
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
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&& [| (i < n_pre) |]
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@ -2258,7 +2257,174 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
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** (store_uint_array rp_pre i l' )
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** (store_uint_array_rec rp_pre i cap2 l'' )
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|--
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
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[| (0 <= i) |]
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&& [| (i < n_pre) |]
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&& [| (n_pre <= cap2) |]
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&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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&& [| (list_store_Z_compact l_2 val ) |]
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&& [| (n_pre <= cap1) |]
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&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
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&& [| (list_store_Z l' val2 ) |]
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&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
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&& [| ((Zlength (l')) = i) |]
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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_compact l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (cap2 <= 100000000) |]
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (store_uint_array rp_pre i l' )
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** (store_uint_array_rec rp_pre i cap2 l'' )
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** (store_uint_array ap_pre n_pre l_2 )
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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.
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Definition mpn_add_1_partial_solve_wit_4 := mpn_add_1_partial_solve_wit_4_pure -> mpn_add_1_partial_solve_wit_4_aux.
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Definition mpn_add_1_partial_solve_wit_5_pure :=
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forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
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[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
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&& [| (i < n_pre) |]
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&& [| (0 <= i) |]
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&& [| (i <= n_pre) |]
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&& [| (list_store_Z_compact l_2 val ) |]
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&& [| (n_pre <= cap1) |]
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&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
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&& [| (list_store_Z l' val2 ) |]
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&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
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&& [| ((Zlength (l')) = i) |]
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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_compact l val ) |]
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&& [| ((Zlength (l2)) = cap2) |]
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&& [| (cap2 >= n_pre) |]
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&& [| (cap1 <= 100000000) |]
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&& [| (cap2 <= 100000000) |]
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&& [| (n_pre > 0) |]
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&& [| (n_pre <= cap1) |]
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&& (store_uint_array ap_pre n_pre l_2 )
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** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
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** ((( &( "i" ) )) # Int |-> i)
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** (store_undef_uint_array_rec ap_pre n_pre cap1 )
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** (store_uint_array rp_pre i l' )
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** (store_uint_array_rec rp_pre i cap2 l'' )
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** ((( &( "b" ) )) # UInt |-> 1)
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** ((( &( "n" ) )) # Int |-> n_pre)
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** ((( &( "ap" ) )) # Ptr |-> ap_pre)
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** ((( &( "rp" ) )) # Ptr |-> rp_pre)
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|--
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[| (0 <= i) |]
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&& [| (i < n_pre) |]
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&& [| (n_pre <= cap2) |]
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.
|
||||
|
||||
Definition mpn_add_1_partial_solve_wit_5_aux :=
|
||||
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
|
||||
[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i <= n_pre) |]
|
||||
&& [| (list_store_Z_compact l_2 val ) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
|
||||
&& [| (list_store_Z l' val2 ) |]
|
||||
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
|
||||
&& [| ((Zlength (l')) = i) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| ((Zlength (l)) = n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (list_store_Z_compact l val ) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (cap2 >= n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (cap2 <= 100000000) |]
|
||||
&& [| (n_pre > 0) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& (store_uint_array ap_pre n_pre l_2 )
|
||||
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
||||
** (store_uint_array rp_pre i l' )
|
||||
** (store_uint_array_rec rp_pre i cap2 l'' )
|
||||
|--
|
||||
[| (0 <= i) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (n_pre <= cap2) |]
|
||||
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i <= n_pre) |]
|
||||
&& [| (list_store_Z_compact l_2 val ) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
|
||||
&& [| (list_store_Z l' val2 ) |]
|
||||
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
|
||||
&& [| ((Zlength (l')) = i) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| ((Zlength (l)) = n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (list_store_Z_compact l val ) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (cap2 >= n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (cap2 <= 100000000) |]
|
||||
&& [| (n_pre > 0) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& (store_uint_array rp_pre i l' )
|
||||
** (store_uint_array_rec rp_pre i cap2 l'' )
|
||||
** (store_uint_array ap_pre n_pre l_2 )
|
||||
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
||||
.
|
||||
|
||||
Definition mpn_add_1_partial_solve_wit_5 := mpn_add_1_partial_solve_wit_5_pure -> mpn_add_1_partial_solve_wit_5_aux.
|
||||
|
||||
Definition mpn_add_1_partial_solve_wit_6 :=
|
||||
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
|
||||
[| (l'' = (cons (a) (l'''))) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (n_pre <= cap2) |]
|
||||
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i <= n_pre) |]
|
||||
&& [| (list_store_Z_compact l_2 val ) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
|
||||
&& [| (list_store_Z l' val2 ) |]
|
||||
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
|
||||
&& [| ((Zlength (l')) = i) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| ((Zlength (l)) = n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (list_store_Z_compact l val ) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (cap2 >= n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (cap2 <= 100000000) |]
|
||||
&& [| (n_pre > 0) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
|
||||
** (store_uint_array rp_pre (i + 1 ) (app (l') ((cons (a) (nil)))) )
|
||||
** (store_uint_array ap_pre n_pre l_2 )
|
||||
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
||||
|--
|
||||
[| (l'' = (cons (a) (l'''))) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (n_pre <= cap2) |]
|
||||
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i <= n_pre) |]
|
||||
@ -2280,10 +2446,74 @@ forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@
|
||||
&& [| (n_pre > 0) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& (((rp_pre + (i * sizeof(UINT) ) )) # UInt |->_)
|
||||
** (store_uint_array_missing_i_rec rp_pre i i cap2 l'' )
|
||||
** (store_uint_array_missing_i_rec rp_pre i 0 (i + 1 ) (app (l') ((cons (a) (nil)))) )
|
||||
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
|
||||
** (store_uint_array ap_pre n_pre l_2 )
|
||||
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
||||
.
|
||||
|
||||
Definition mpn_add_1_partial_solve_wit_7 :=
|
||||
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
|
||||
[| (l'' = (cons (a) (l'''))) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (n_pre <= cap2) |]
|
||||
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i <= n_pre) |]
|
||||
&& [| (list_store_Z_compact l_2 val ) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
|
||||
&& [| (list_store_Z l' val2 ) |]
|
||||
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
|
||||
&& [| ((Zlength (l')) = i) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| ((Zlength (l)) = n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (list_store_Z_compact l val ) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (cap2 >= n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (cap2 <= 100000000) |]
|
||||
&& [| (n_pre > 0) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
|
||||
** (store_uint_array rp_pre (i + 1 ) (app (l') ((cons (a) (nil)))) )
|
||||
** (store_uint_array ap_pre n_pre l_2 )
|
||||
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
||||
|--
|
||||
[| (l'' = (cons (a) (l'''))) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (n_pre <= cap2) |]
|
||||
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i <= n_pre) |]
|
||||
&& [| (list_store_Z_compact l_2 val ) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
|
||||
&& [| (list_store_Z l' val2 ) |]
|
||||
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
|
||||
&& [| ((Zlength (l')) = i) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& [| ((Zlength (l)) = n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (list_store_Z_compact l val ) |]
|
||||
&& [| ((Zlength (l2)) = cap2) |]
|
||||
&& [| (cap2 >= n_pre) |]
|
||||
&& [| (cap1 <= 100000000) |]
|
||||
&& [| (cap2 <= 100000000) |]
|
||||
&& [| (n_pre > 0) |]
|
||||
&& [| (n_pre <= cap1) |]
|
||||
&& (((rp_pre + (i * sizeof(UINT) ) )) # UInt |->_)
|
||||
** (store_uint_array_missing_i_rec rp_pre i 0 (i + 1 ) (app (l') ((cons (a) (nil)))) )
|
||||
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
|
||||
** (store_uint_array ap_pre n_pre l_2 )
|
||||
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|
||||
** (store_uint_array rp_pre i l' )
|
||||
.
|
||||
|
||||
Definition mpn_add_1_which_implies_wit_1 :=
|
||||
@ -2309,6 +2539,23 @@ forall (rp_pre: Z) (cap2: Z) (l2: (@list Z)) ,
|
||||
** (store_uint_array rp_pre 0 nil )
|
||||
.
|
||||
|
||||
Definition mpn_add_1_which_implies_wit_3 :=
|
||||
forall (n_pre: Z) (rp_pre: Z) (cap2: Z) (l'': (@list Z)) (l': (@list Z)) (i: Z) ,
|
||||
[| (0 <= i) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (n_pre <= cap2) |]
|
||||
&& (store_uint_array rp_pre i l' )
|
||||
** (store_uint_array_rec rp_pre i cap2 l'' )
|
||||
|--
|
||||
EX (a: Z) (l''': (@list Z)) ,
|
||||
[| (l'' = (cons (a) (l'''))) |]
|
||||
&& [| (0 <= i) |]
|
||||
&& [| (i < n_pre) |]
|
||||
&& [| (n_pre <= cap2) |]
|
||||
&& (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
|
||||
** (store_uint_array rp_pre (i + 1 ) (app (l') ((cons (a) (nil)))) )
|
||||
.
|
||||
|
||||
Module Type VC_Correct.
|
||||
|
||||
Axiom proof_of_gmp_abs_safety_wit_1 : gmp_abs_safety_wit_1.
|
||||
@ -2390,9 +2637,14 @@ Axiom proof_of_mpn_add_1_partial_solve_wit_1 : mpn_add_1_partial_solve_wit_1.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_2_pure : mpn_add_1_partial_solve_wit_2_pure.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_2 : mpn_add_1_partial_solve_wit_2.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_3 : mpn_add_1_partial_solve_wit_3.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_4_pure : mpn_add_1_partial_solve_wit_4_pure.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_4 : mpn_add_1_partial_solve_wit_4.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_5_pure : mpn_add_1_partial_solve_wit_5_pure.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_5 : mpn_add_1_partial_solve_wit_5.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_6 : mpn_add_1_partial_solve_wit_6.
|
||||
Axiom proof_of_mpn_add_1_partial_solve_wit_7 : mpn_add_1_partial_solve_wit_7.
|
||||
Axiom proof_of_mpn_add_1_which_implies_wit_1 : mpn_add_1_which_implies_wit_1.
|
||||
Axiom proof_of_mpn_add_1_which_implies_wit_2 : mpn_add_1_which_implies_wit_2.
|
||||
Axiom proof_of_mpn_add_1_which_implies_wit_3 : mpn_add_1_which_implies_wit_3.
|
||||
|
||||
End VC_Correct.
|
||||
|
@ -164,9 +164,21 @@ Proof. Admitted.
|
||||
Lemma proof_of_mpn_add_1_partial_solve_wit_3 : mpn_add_1_partial_solve_wit_3.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_partial_solve_wit_4_pure : mpn_add_1_partial_solve_wit_4_pure.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_partial_solve_wit_4 : mpn_add_1_partial_solve_wit_4.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_partial_solve_wit_5_pure : mpn_add_1_partial_solve_wit_5_pure.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_partial_solve_wit_5 : mpn_add_1_partial_solve_wit_5.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_partial_solve_wit_6 : mpn_add_1_partial_solve_wit_6.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_partial_solve_wit_7 : mpn_add_1_partial_solve_wit_7.
|
||||
Proof. Admitted.
|
||||
|
||||
|
@ -407,13 +407,119 @@ Proof.
|
||||
Qed.
|
||||
|
||||
Lemma proof_of_mpn_add_1_entail_wit_1 : mpn_add_1_entail_wit_1.
|
||||
Proof. Admitted.
|
||||
Proof.
|
||||
pre_process.
|
||||
Exists l2 nil 0 0 l_2.
|
||||
entailer!.
|
||||
- unfold list_store_Z.
|
||||
split.
|
||||
+ simpl. tauto.
|
||||
+ simpl. tauto.
|
||||
- rewrite (sublist_nil l_2 0 0); try lia.
|
||||
unfold list_store_Z.
|
||||
split.
|
||||
+ simpl. tauto.
|
||||
+ simpl. tauto.
|
||||
Qed.
|
||||
|
||||
Lemma proof_of_mpn_add_1_entail_wit_2_1 : mpn_add_1_entail_wit_2_1.
|
||||
Proof. Admitted.
|
||||
Proof.
|
||||
pre_process.
|
||||
rewrite replace_Znth_app_r.
|
||||
- Exists l'''.
|
||||
rewrite H12.
|
||||
assert (i - i = 0) by lia.
|
||||
rewrite H24.
|
||||
set (new_b := (unsigned_last_nbits (Znth i l_3 0 + b) 32)).
|
||||
rewrite replace_Znth_nothing; try lia.
|
||||
assert (replace_Znth 0 new_b (a :: nil) = new_b :: nil). {
|
||||
unfold replace_Znth.
|
||||
unfold Z.to_nat.
|
||||
unfold replace_nth.
|
||||
reflexivity.
|
||||
}
|
||||
rewrite H25.
|
||||
Exists (l'_2 ++ new_b :: nil).
|
||||
Exists (val2_2 + new_b * (UINT_MOD^ i)).
|
||||
Exists (val1_2 + (Znth i l_3 0) * (UINT_MOD^ i)).
|
||||
Exists l_3.
|
||||
entailer!.
|
||||
+ rewrite Zlength_app.
|
||||
rewrite H12.
|
||||
unfold Zlength.
|
||||
unfold Zlength_aux.
|
||||
lia.
|
||||
+ assert (val1_2 + Znth i l_3 0 * 4294967296 ^ i + b_pre = (val1_2 + b_pre) + Znth i l_3 0 * 4294967296 ^ i) by lia.
|
||||
rewrite H26.
|
||||
rewrite <- H11.
|
||||
assert (Znth i l_3 0 + b = new_b + UINT_MOD).
|
||||
{
|
||||
subst new_b.
|
||||
unfold unsigned_last_nbits.
|
||||
unfold unsigned_last_nbits in H3.
|
||||
assert (2^32 = 4294967296). { nia. }
|
||||
rewrite H27 in *.
|
||||
admit.
|
||||
}
|
||||
admit.
|
||||
+ pose proof (__list_store_Z_concat_r l'_2 val2_2 new_b).
|
||||
apply H26 in H10.
|
||||
rewrite H12 in H10.
|
||||
assert (new_b * 4294967296 ^ i + val2_2 = (val2_2 + new_b * 4294967296 ^ i)) by lia.
|
||||
rewrite H27 in H10.
|
||||
tauto.
|
||||
subst new_b.
|
||||
unfold unsigned_last_nbits.
|
||||
assert (2 ^ 32 = 4294967296). { nia. }
|
||||
rewrite H27.
|
||||
apply Z.mod_pos_bound.
|
||||
lia.
|
||||
+ assert (l_2=l_3).
|
||||
{
|
||||
pose proof (list_store_Z_compact_reverse_injection l_2 l_3 val val).
|
||||
apply H26 in H7; try tauto.
|
||||
}
|
||||
|
||||
assert (i < Zlength l_3). {
|
||||
subst l_3.
|
||||
rewrite H15.
|
||||
tauto.
|
||||
}
|
||||
|
||||
assert((sublist 0 (i + 1) l_3) = (sublist 0 i l_3) ++ (Znth i l_3 0) :: nil). {
|
||||
pose proof (sublist_split 0 (i+1) i l_3).
|
||||
pose proof (sublist_single i l_3 0).
|
||||
rewrite <-H29.
|
||||
apply H28.
|
||||
lia.
|
||||
subst l_3.
|
||||
rewrite Zlength_correct in H27.
|
||||
lia.
|
||||
rewrite Zlength_correct in H27.
|
||||
lia.
|
||||
}
|
||||
rewrite H28.
|
||||
pose proof (__list_store_Z_concat_r (sublist 0 i l_3) val1_2 (Znth i l_3 0)).
|
||||
apply H29 in H9.
|
||||
rewrite Zlength_sublist0 in H9.
|
||||
assert (val1_2 + Znth i l_3 0 * 4294967296 ^ i = Znth i l_3 0 * 4294967296 ^ i + val1_2) by lia.
|
||||
rewrite H30.
|
||||
tauto.
|
||||
subst l_3.
|
||||
rewrite H15.
|
||||
lia.
|
||||
apply list_within_bound_Znth.
|
||||
lia.
|
||||
unfold list_store_Z_compact in H7.
|
||||
tauto.
|
||||
- pose proof (Zlength_sublist0 i l'_2).
|
||||
lia.
|
||||
Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_entail_wit_2_2 : mpn_add_1_entail_wit_2_2.
|
||||
Proof. Admitted.
|
||||
Proof.
|
||||
pre_process.
|
||||
Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_return_wit_1 : mpn_add_1_return_wit_1.
|
||||
Proof.
|
||||
@ -455,4 +561,7 @@ Lemma proof_of_mpn_add_1_which_implies_wit_1 : mpn_add_1_which_implies_wit_1.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_which_implies_wit_2 : mpn_add_1_which_implies_wit_2.
|
||||
Proof. Admitted.
|
||||
|
||||
Lemma proof_of_mpn_add_1_which_implies_wit_3 : mpn_add_1_which_implies_wit_3.
|
||||
Proof. Admitted.
|
Reference in New Issue
Block a user