Commit 9ddbd8d7 by MARCHE Claude

Update sessions: enforce Alt-Ergo 0.95.2 in some use of why3 Coq tactic

parent df3b3fe9
 ... ... @@ -4,8 +4,8 @@ ... ... @@ -16,28 +16,28 @@ ... ... @@ -63,50 +63,49 @@ ... ... @@ -120,8 +119,8 @@ ... ... @@ -130,8 +129,8 @@ ... ... @@ -140,8 +139,8 @@ ... ... @@ -151,8 +150,8 @@ ... ... @@ -161,8 +160,8 @@ ... ... @@ -171,8 +170,8 @@ ... ... @@ -182,8 +181,8 @@ ... ... @@ -284,8 +283,8 @@ ... ...
 ... ... @@ -152,15 +152,19 @@ Axiom pow2_62 : ((pow2 62%Z) = 4611686018427387904%Z). Axiom pow2_63 : ((pow2 63%Z) = 9223372036854775808%Z). Axiom Div_double : forall (x:Z) (y:Z), (((0%Z < y)%Z /\ (y <= x)%Z) /\ (x < (2%Z * y)%Z)%Z) -> ((int.EuclideanDivision.div x y) = 1%Z). Axiom Div_mult_inst : forall (x:Z) (z:Z), (0%Z < x)%Z -> ((int.EuclideanDivision.div ((x * 1%Z)%Z + z)%Z x) = (1%Z + (int.EuclideanDivision.div z x))%Z). Axiom Div_double : forall (x:Z) (y:Z), ((0%Z < y)%Z /\ ((y <= x)%Z /\ (x < (2%Z * y)%Z)%Z)) -> ((int.EuclideanDivision.div x y) = 1%Z). Axiom Div_pow : forall (x:Z) (i:Z), (0%Z < i)%Z -> ((((pow2 (i - 1%Z)%Z) <= x)%Z /\ (x < (pow2 i))%Z) -> ((int.EuclideanDivision.div x (pow2 (i - 1%Z)%Z)) = 1%Z)). Axiom Div_double_neg : forall (x:Z) (y:Z), (((((-2%Z)%Z * y)%Z <= x)%Z /\ (x < (-y)%Z)%Z) /\ ((-y)%Z < 0%Z)%Z) -> ((int.EuclideanDivision.div x Axiom Div_double_neg : forall (x:Z) (y:Z), ((((-2%Z)%Z * y)%Z <= x)%Z /\ ((x < (-y)%Z)%Z /\ ((-y)%Z < 0%Z)%Z)) -> ((int.EuclideanDivision.div x y) = (-2%Z)%Z). Axiom Div_pow2 : forall (x:Z) (i:Z), (0%Z < i)%Z -> ... ... @@ -188,7 +192,7 @@ Axiom Power_s_all : forall (n:Z), Axiom Power_p_all : forall (n:Z), ((pow21 (n - 1%Z)%Z) = ((05 / 10)%R * (pow21 n))%R). Axiom Power_1_2 : ((05 / 10)%R = (Rdiv 1%R 2%R)%R). Axiom Power_1_2 : ((05 / 10)%R = (1%R / 2%R)%R). Axiom Power_11 : ((pow21 1%Z) = 2%R). ... ... @@ -197,11 +201,11 @@ Axiom Power_neg1 : ((pow21 (-1%Z)%Z) = (05 / 10)%R). Axiom Power_non_null_aux : forall (n:Z), (0%Z <= n)%Z -> ~ ((pow21 n) = 0%R). Axiom Power_neg_aux : forall (n:Z), (0%Z <= n)%Z -> ((pow21 (-n)%Z) = (Rdiv 1%R (pow21 n))%R). ((pow21 (-n)%Z) = (1%R / (pow21 n))%R). Axiom Power_non_null : forall (n:Z), ~ ((pow21 n) = 0%R). Axiom Power_neg : forall (n:Z), ((pow21 (-n)%Z) = (Rdiv 1%R (pow21 n))%R). Axiom Power_neg : forall (n:Z), ((pow21 (-n)%Z) = (1%R / (pow21 n))%R). Axiom Power_sum_aux : forall (n:Z) (m:Z), (0%Z <= m)%Z -> ((pow21 (n + m)%Z) = ((pow21 n) * (pow21 m))%R). ... ... @@ -210,7 +214,7 @@ Axiom Power_sum1 : forall (n:Z) (m:Z), ((pow21 (n + m)%Z) = ((pow21 n) * (pow21 m))%R). Axiom Pow2_int_real : forall (x:Z), (0%Z <= x)%Z -> ((pow21 x) = (IZR (pow2 x))). ((pow21 x) = (Reals.Raxioms.IZR (pow2 x))). Axiom size_positive : (1%Z < 32%Z)%Z. ... ... @@ -239,21 +243,24 @@ Axiom extensionality : forall (v1:bv) (v2:bv), (eq v1 v2) -> (v1 = v2). Parameter bw_and: bv -> bv -> bv. Axiom Nth_bw_and : forall (v1:bv) (v2:bv) (n:Z), ((0%Z <= n)%Z /\ (n < 32%Z)%Z) -> ((nth (bw_and v1 v2) n) = (andb (nth v1 n) (nth v2 n))). (n < 32%Z)%Z) -> ((nth (bw_and v1 v2) n) = (Init.Datatypes.andb (nth v1 n) (nth v2 n))). Parameter bw_or: bv -> bv -> bv. Axiom Nth_bw_or : forall (v1:bv) (v2:bv) (n:Z), ((0%Z <= n)%Z /\ (n < 32%Z)%Z) -> ((nth (bw_or v1 v2) n) = (orb (nth v1 n) (nth v2 n))). (n < 32%Z)%Z) -> ((nth (bw_or v1 v2) n) = (Init.Datatypes.orb (nth v1 n) (nth v2 n))). Parameter bw_xor: bv -> bv -> bv. Axiom Nth_bw_xor : forall (v1:bv) (v2:bv) (n:Z), ((0%Z <= n)%Z /\ (n < 32%Z)%Z) -> ((nth (bw_xor v1 v2) n) = (xorb (nth v1 n) (nth v2 n))). (n < 32%Z)%Z) -> ((nth (bw_xor v1 v2) n) = (Init.Datatypes.xorb (nth v1 n) (nth v2 n))). Axiom Nth_bw_xor_v1true : forall (v1:bv) (v2:bv) (n:Z), (((0%Z <= n)%Z /\ (n < 32%Z)%Z) /\ ((nth v1 n) = true)) -> ((nth (bw_xor v1 v2) n) = (negb (nth v2 n))). n) = (Init.Datatypes.negb (nth v2 n))). Axiom Nth_bw_xor_v1false : forall (v1:bv) (v2:bv) (n:Z), (((0%Z <= n)%Z /\ (n < 32%Z)%Z) /\ ((nth v1 n) = false)) -> ((nth (bw_xor v1 v2) n) = (nth v2 ... ... @@ -261,7 +268,7 @@ Axiom Nth_bw_xor_v1false : forall (v1:bv) (v2:bv) (n:Z), (((0%Z <= n)%Z /\ Axiom Nth_bw_xor_v2true : forall (v1:bv) (v2:bv) (n:Z), (((0%Z <= n)%Z /\ (n < 32%Z)%Z) /\ ((nth v2 n) = true)) -> ((nth (bw_xor v1 v2) n) = (negb (nth v1 n))). n) = (Init.Datatypes.negb (nth v1 n))). Axiom Nth_bw_xor_v2false : forall (v1:bv) (v2:bv) (n:Z), (((0%Z <= n)%Z /\ (n < 32%Z)%Z) /\ ((nth v2 n) = false)) -> ((nth (bw_xor v1 v2) n) = (nth v1 ... ... @@ -270,7 +277,7 @@ Axiom Nth_bw_xor_v2false : forall (v1:bv) (v2:bv) (n:Z), (((0%Z <= n)%Z /\ Parameter bw_not: bv -> bv. Axiom Nth_bw_not : forall (v:bv) (n:Z), ((0%Z <= n)%Z /\ (n < 32%Z)%Z) -> ((nth (bw_not v) n) = (negb (nth v n))). ((nth (bw_not v) n) = (Init.Datatypes.negb (nth v n))). Parameter lsr: bv -> Z -> bv. ... ... @@ -304,19 +311,19 @@ Axiom lsl_nth_low : forall (b:bv) (n:Z) (s:Z), ((0%Z <= n)%Z /\ Parameter to_nat_sub: bv -> Z -> Z -> Z. Axiom to_nat_sub_zero : forall (b:bv) (j:Z) (i:Z), (((0%Z <= i)%Z /\ (i <= j)%Z) /\ (j < 32%Z)%Z) -> (((nth b j) = false) -> ((to_nat_sub b j Axiom to_nat_sub_zero : forall (b:bv) (j:Z) (i:Z), ((0%Z <= i)%Z /\ ((i <= j)%Z /\ (j < 32%Z)%Z)) -> (((nth b j) = false) -> ((to_nat_sub b j i) = (to_nat_sub b (j - 1%Z)%Z i))). Axiom to_nat_sub_one : forall (b:bv) (j:Z) (i:Z), (((0%Z <= i)%Z /\ (i <= j)%Z) /\ (j < 32%Z)%Z) -> (((nth b j) = true) -> ((to_nat_sub b j Axiom to_nat_sub_one : forall (b:bv) (j:Z) (i:Z), ((0%Z <= i)%Z /\ ((i <= j)%Z /\ (j < 32%Z)%Z)) -> (((nth b j) = true) -> ((to_nat_sub b j i) = ((pow2 (j - i)%Z) + (to_nat_sub b (j - 1%Z)%Z i))%Z)). Axiom to_nat_sub_high : forall (b:bv) (j:Z) (i:Z), (j < i)%Z -> ((to_nat_sub b j i) = 0%Z). Axiom to_nat_of_zero2 : forall (b:bv) (i:Z) (j:Z), (((j < 32%Z)%Z /\ (i <= j)%Z) /\ (0%Z <= i)%Z) -> ((forall (k:Z), ((k <= j)%Z /\ Axiom to_nat_of_zero2 : forall (b:bv) (i:Z) (j:Z), ((j < 32%Z)%Z /\ ((i <= j)%Z /\ (0%Z <= i)%Z)) -> ((forall (k:Z), ((k <= j)%Z /\ (i < k)%Z) -> ((nth b k) = false)) -> ((to_nat_sub b j 0%Z) = (to_nat_sub b i 0%Z))). ... ... @@ -324,8 +331,8 @@ Axiom to_nat_of_zero : forall (b:bv) (i:Z) (j:Z), ((j < 32%Z)%Z /\ (0%Z <= i)%Z) -> ((forall (k:Z), ((k <= j)%Z /\ (i <= k)%Z) -> ((nth b k) = false)) -> ((to_nat_sub b j i) = 0%Z)). Axiom to_nat_of_one : forall (b:bv) (i:Z) (j:Z), (((j < 32%Z)%Z /\ (i <= j)%Z) /\ (0%Z <= i)%Z) -> ((forall (k:Z), ((k <= j)%Z /\ Axiom to_nat_of_one : forall (b:bv) (i:Z) (j:Z), ((j < 32%Z)%Z /\ ((i <= j)%Z /\ (0%Z <= i)%Z)) -> ((forall (k:Z), ((k <= j)%Z /\ (i <= k)%Z) -> ((nth b k) = true)) -> ((to_nat_sub b j i) = ((pow2 ((j - i)%Z + 1%Z)%Z) - 1%Z)%Z)). ... ... @@ -413,23 +420,24 @@ Axiom extensionality1 : forall (v1:bv1) (v2:bv1), (eq1 v1 v2) -> (v1 = v2). Parameter bw_and1: bv1 -> bv1 -> bv1. Axiom Nth_bw_and1 : forall (v1:bv1) (v2:bv1) (n:Z), ((0%Z <= n)%Z /\ (n < 64%Z)%Z) -> ((nth1 (bw_and1 v1 v2) n) = (andb (nth1 v1 n) (nth1 v2 n))). (n < 64%Z)%Z) -> ((nth1 (bw_and1 v1 v2) n) = (Init.Datatypes.andb (nth1 v1 n) (nth1 v2 n))). Parameter bw_or1: bv1 -> bv1 -> bv1. Axiom Nth_bw_or1 : forall (v1:bv1) (v2:bv1) (n:Z), ((0%Z <= n)%Z /\ (n < 64%Z)%Z) -> ((nth1 (bw_or1 v1 v2) n) = (orb (nth1 v1 n) (nth1 v2 n))). (n < 64%Z)%Z) -> ((nth1 (bw_or1 v1 v2) n) = (Init.Datatypes.orb (nth1 v1 n) (nth1 v2 n))). Parameter bw_xor1: bv1 -> bv1 -> bv1. Axiom Nth_bw_xor1 : forall (v1:bv1) (v2:bv1) (n:Z), ((0%Z <= n)%Z /\ (n < 64%Z)%Z) -> ((nth1 (bw_xor1 v1 v2) n) = (xorb (nth1 v1 n) (nth1 v2 n))). (n < 64%Z)%Z) -> ((nth1 (bw_xor1 v1 v2) n) = (Init.Datatypes.xorb (nth1 v1 n) (nth1 v2 n))). Axiom Nth_bw_xor_v1true1 : forall (v1:bv1) (v2:bv1) (n:Z), (((0%Z <= n)%Z /\ (n < 64%Z)%Z) /\ ((nth1 v1 n) = true)) -> ((nth1 (bw_xor1 v1 v2) n) = (negb (nth1 v2 n))). n) = (Init.Datatypes.negb (nth1 v2 n))). Axiom Nth_bw_xor_v1false1 : forall (v1:bv1) (v2:bv1) (n:Z), (((0%Z <= n)%Z /\ (n < 64%Z)%Z) /\ ((nth1 v1 n) = false)) -> ((nth1 (bw_xor1 v1 v2) ... ... @@ -437,7 +445,7 @@ Axiom Nth_bw_xor_v1false1 : forall (v1:bv1) (v2:bv1) (n:Z), (((0%Z <= n)%Z /\ Axiom Nth_bw_xor_v2true1 : forall (v1:bv1) (v2:bv1) (n:Z), (((0%Z <= n)%Z /\ (n < 64%Z)%Z) /\ ((nth1 v2 n) = true)) -> ((nth1 (bw_xor1 v1 v2) n) = (negb (nth1 v1 n))). n) = (Init.Datatypes.negb (nth1 v1 n))). Axiom Nth_bw_xor_v2false1 : forall (v1:bv1) (v2:bv1) (n:Z), (((0%Z <= n)%Z /\ (n < 64%Z)%Z) /\ ((nth1 v2 n) = false)) -> ((nth1 (bw_xor1 v1 v2) ... ... @@ -446,7 +454,7 @@ Axiom Nth_bw_xor_v2false1 : forall (v1:bv1) (v2:bv1) (n:Z), (((0%Z <= n)%Z /\ Parameter bw_not1: bv1 -> bv1. Axiom Nth_bw_not1 : forall (v:bv1) (n:Z), ((0%Z <= n)%Z /\ (n < 64%Z)%Z) -> ((nth1 (bw_not1 v) n) = (negb (nth1 v n))). ((nth1 (bw_not1 v) n) = (Init.Datatypes.negb (nth1 v n))). Parameter lsr1: bv1 -> Z -> bv1. ... ... @@ -480,19 +488,19 @@ Axiom lsl_nth_low1 : forall (b:bv1) (n:Z) (s:Z), ((0%Z <= n)%Z /\ Parameter to_nat_sub1: bv1 -> Z -> Z -> Z. Axiom to_nat_sub_zero1 : forall (b:bv1) (j:Z) (i:Z), (((0%Z <= i)%Z /\ (i <= j)%Z) /\ (j < 64%Z)%Z) -> (((nth1 b j) = false) -> ((to_nat_sub1 b j Axiom to_nat_sub_zero1 : forall (b:bv1) (j:Z) (i:Z), ((0%Z <= i)%Z /\ ((i <= j)%Z /\ (j < 64%Z)%Z)) -> (((nth1 b j) = false) -> ((to_nat_sub1 b j i) = (to_nat_sub1 b (j - 1%Z)%Z i))). Axiom to_nat_sub_one1 : forall (b:bv1) (j:Z) (i:Z), (((0%Z <= i)%Z /\ (i <= j)%Z) /\ (j < 64%Z)%Z) -> (((nth1 b j) = true) -> ((to_nat_sub1 b j Axiom to_nat_sub_one1 : forall (b:bv1) (j:Z) (i:Z), ((0%Z <= i)%Z /\ ((i <= j)%Z /\ (j < 64%Z)%Z)) -> (((nth1 b j) = true) -> ((to_nat_sub1 b j i) = ((pow2 (j - i)%Z) + (to_nat_sub1 b (j - 1%Z)%Z i))%Z)). Axiom to_nat_sub_high1 : forall (b:bv1) (j:Z) (i:Z), (j < i)%Z -> ((to_nat_sub1 b j i) = 0%Z). Axiom to_nat_of_zero21 : forall (b:bv1) (i:Z) (j:Z), (((j < 64%Z)%Z /\ (i <= j)%Z) /\ (0%Z <= i)%Z) -> ((forall (k:Z), ((k <= j)%Z /\ Axiom to_nat_of_zero21 : forall (b:bv1) (i:Z) (j:Z), ((j < 64%Z)%Z /\ ((i <= j)%Z /\ (0%Z <= i)%Z)) -> ((forall (k:Z), ((k <= j)%Z /\ (i < k)%Z) -> ((nth1 b k) = false)) -> ((to_nat_sub1 b j 0%Z) = (to_nat_sub1 b i 0%Z))). ... ... @@ -500,8 +508,8 @@ Axiom to_nat_of_zero1 : forall (b:bv1) (i:Z) (j:Z), ((j < 64%Z)%Z /\ (0%Z <= i)%Z) -> ((forall (k:Z), ((k <= j)%Z /\ (i <= k)%Z) -> ((nth1 b k) = false)) -> ((to_nat_sub1 b j i) = 0%Z)). Axiom to_nat_of_one1 : forall (b:bv1) (i:Z) (j:Z), (((j < 64%Z)%Z /\ (i <= j)%Z) /\ (0%Z <= i)%Z) -> ((forall (k:Z), ((k <= j)%Z /\ Axiom to_nat_of_one1 : forall (b:bv1) (i:Z) (j:Z), ((j < 64%Z)%Z /\ ((i <= j)%Z /\ (0%Z <= i)%Z)) -> ((forall (k:Z), ((k <= j)%Z /\ (i <= k)%Z) -> ((nth1 b k) = true)) -> ((to_nat_sub1 b j i) = ((pow2 ((j - i)%Z + 1%Z)%Z) - 1%Z)%Z)). ... ... @@ -590,7 +598,7 @@ Axiom sign_of_double_negative : forall (b:bv1), ((nth1 b 63%Z) = true) -> Axiom double_of_bv64_value : forall (b:bv1), ((0%Z < (to_nat_sub1 b 62%Z 52%Z))%Z /\ ((to_nat_sub1 b 62%Z 52%Z) < 2047%Z)%Z) -> ((double_of_bv64 b) = (((sign_value (nth1 b 63%Z)) * (pow21 ((to_nat_sub1 b 62%Z 52%Z) - 1023%Z)%Z))%R * (1%R + ((IZR (to_nat_sub1 b 51%Z 62%Z 52%Z) - 1023%Z)%Z))%R * (1%R + ((Reals.Raxioms.IZR (to_nat_sub1 b 51%Z 0%Z)) * (pow21 (-52%Z)%Z))%R)%R)%R). Axiom nth_j1 : forall (i:Z), ((0%Z <= i)%Z /\ (i <= 19%Z)%Z) -> ... ... @@ -667,7 +675,7 @@ Axiom mantissa_const_to_nat51 : ((to_nat_sub1 (concat (from_int 1127219200%Z) Axiom mantissa_const : ((to_nat_sub1 (concat (from_int 1127219200%Z) (from_int 2147483648%Z)) 51%Z 0%Z) = (pow2 31%Z)). Axiom real1075m1023 : ((IZR (1075%Z - 1023%Z)%Z) = 52%R). Axiom real1075m1023 : ((Reals.Raxioms.IZR (1075%Z - 1023%Z)%Z) = 52%R). Axiom real1075m1023_2 : ((1075%R - 1023%R)%R = 52%R). ... ... @@ -702,7 +710,7 @@ Axiom nth_jpxor_0_30 : forall (x:Z), forall (i:Z), ((is_int32 x) /\ i) = (nth (from_int2c x) i)). Axiom nth_var31 : forall (x:Z), ((nth (jpxor x) 31%Z) = (negb (nth (from_int2c x) 31%Z))). 31%Z) = (Init.Datatypes.negb (nth (from_int2c x) 31%Z))). Axiom to_nat_sub_0_30 : forall (x:Z), (is_int32 x) -> ((to_nat_sub (bw_xor (from_int 2147483648%Z) (from_int2c x)) 30%Z ... ... @@ -752,7 +760,7 @@ Axiom nth_var3 : forall (x:Z) (i:Z), ((is_int32 x) /\ ((32%Z <= i)%Z /\ Open Scope Z_scope. Require Import Why3. Ltac ae := why3 "alt-ergo" timelimit 30. Ltac ae := why3 "Alt-Ergo,0.95.2," timelimit 30. (* Why3 goal *) Theorem lemma2 : forall (x:Z), (is_int32 x) -> ((to_nat_sub1 (var x) 51%Z ... ... @@ -764,4 +772,3 @@ ae. ae. Qed.
 ... ... @@ -11,66 +11,66 @@