Commit 4c831e45 by MARCHE Claude

### fix unused quantified variables

parent 942829fd
 ... ... @@ -3,7 +3,7 @@ theory A type t axiom Ax : forall x:t. true axiom Ax : forall x:t. x=x end theory B ... ...
 ... ... @@ -4,5 +4,5 @@ theory MinMax goal G : forall x y z : t. ge z y -> ge z x -> ge y x -> min x (max (min z x) y) = x goal G2 : forall x y z : t. max x y = x -> ge x y goal G2 : forall x y: t. max x y = x -> ge x y end \ No newline at end of file
 ... ... @@ -37,7 +37,7 @@ theory LambdaCalc forall t : term 'b. subst (Var j) i t = if i = j then t else (Var j) (* correct ?*) axiom Subst_def1 : forall i j : nat. axiom Subst_def1 : forall i : nat. forall t : term 'b. subst (Var i) i t = t axiom Subst_def2 : forall t1 : term 'a. forall i : nat. ... ... @@ -48,7 +48,7 @@ theory LambdaCalc function app (t1 : term 'a) (t2 : term 'b) : term 'a axiom App_def : forall t1 : term 'a. forall i : nat. forall t2 : term 'b. forall t1 : term 'a. forall t2 : term 'b. app (Lambda t1) t2 = subst t1 Zero t2 (* When we remove one of the following example the axiomatic is not anymore inconsistent *) ... ... @@ -142,7 +142,7 @@ theory LambdaCalc2 function app (t1 : app 'b 'a) (t2 : 'b) : 'a axiom App_def : forall t1 : 'a. forall i : nat. forall t2 : 'b. forall t1 : 'a. forall t2 : 'b. app (lambda t1) t2 = subst t1 Zero t2 (* axiom Subst_app : *) ... ...
 ... ... @@ -179,7 +179,7 @@ inductive one_step env env expr env env expr = sigma' pi' (Eassign x e') | one_step_assign_value: forall sigma pi:env, x:ident, v:value, e:term. forall sigma pi:env, x:ident, v:value. one_step sigma pi (Eassign x (Evalue v)) (IdMap.set sigma x v) pi void ... ...
 ... ... @@ -232,7 +232,7 @@ inductive one_step env stack expr env stack expr = sigma' pi' (Eassign x e') | one_step_assign_value: forall sigma:env, pi:stack, x:refident, v:value, e:term. forall sigma:env, pi:stack, x:refident, v:value. one_step sigma pi (Eassign x (Evalue v)) (IdMap.set sigma x v) pi void ... ... @@ -242,7 +242,7 @@ inductive one_step env stack expr env stack expr = one_step sigma pi (Eseq e1 e2) sigma' pi' (Eseq e1' e2) | one_step_seq_value: forall sigma:env, pi:stack, id:ident, e:expr. forall sigma:env, pi:stack, e:expr. one_step sigma pi (Eseq void e) sigma pi e | one_step_let_ctxt: ... ... @@ -255,16 +255,16 @@ inductive one_step env stack expr env stack expr = one_step sigma pi (Elet id (Evalue v) e) sigma (Cons (id,v) pi) e | one_step_if_ctxt: forall sigma sigma':env, pi pi':stack, id:ident, e1 e1' e2 e3:expr. forall sigma sigma':env, pi pi':stack, e1 e1' e2 e3:expr. one_step sigma pi e1 sigma' pi' e1' -> one_step sigma pi (Eif e1 e2 e3) sigma' pi' (Eif e1' e2 e3) | one_step_if_true: forall sigma:env, pi:stack, e:term, e1 e2:expr. forall sigma:env, pi:stack, e1 e2:expr. one_step sigma pi (Eif (Evalue (Vbool True)) e1 e2) sigma pi e1 | one_step_if_false: forall sigma:env, pi:stack, e:term, e1 e2:expr. forall sigma:env, pi:stack, e1 e2:expr. one_step sigma pi (Eif (Evalue (Vbool False)) e1 e2) sigma pi e2 | one_step_assert: ... ...
 ... ... @@ -45,11 +45,11 @@ theory FibSumEven "sum of even-valued Fibonacci numbers" (* Note: we take for granted that [fib] is an increasing sequence *) axiom SumYes: forall n m s:int. axiom SumYes: forall n m:int. n >= 0 -> (fib n) < m -> mod (fib n) 2 = 0 -> fib_sum_even_lt_from m n = fib_sum_even_lt_from m (n+1) + (fib n) axiom SumOdd: forall n m s:int. axiom SumOdd: forall n m:int. n >= 0 -> mod (fib n) 2 <> 0 -> fib_sum_even_lt_from m n = fib_sum_even_lt_from m (n+1) ... ...
 ... ... @@ -99,7 +99,7 @@ module M (** Frame for list_disj *) axiom frame_list_disj : forall ft : ft pointer, next : next, forall next : next, p1 : pointer, p2 : pointer, q : pointer, v : pointer [list_disj (list_ft next[q <- v] p1) next[q <- v] p2]. (not in_ft q (list_ft next p1)) -> (not in_ft q (list_ft next p2)) ... ... @@ -148,7 +148,7 @@ module M (** frame model *) axiom frame_model : forall ft : ft pointer, next : next, forall next : next, p : pointer, q : pointer, v : pointer[model next[q <- v] p]. (not in_ft q (list_ft next p)) -> model next p = model next[q <- v] p ... ... @@ -316,7 +316,7 @@ module M2 (** frame model *) lemma frame_model : forall ft : ft pointer, next : next, forall next : next, p : pointer, q : pointer, v : pointer[model next[q <- v] p]. is_list next p -> (not in_ft q (list_ft next p)) -> ... ...
 ... ... @@ -14,10 +14,10 @@ theory Bidule goal Inter : forall s1 s2 : s. forall x : a. mem x (inter s1 s2) -> (mem x s1 /\ mem x s2) goal Union_inter : forall s1 s2 s3 : s. forall x : a. goal Union_inter : forall s1 s2 s3 : s. equal (inter (union s1 s2) s3) (union (inter s1 s3) (inter s2 s3)) lemma Union_assoc : forall s1 s2 s3 : s. forall x : a. lemma Union_assoc : forall s1 s2 s3 : s. equal (union (union s1 s2) s3) (union s1 (union s2 s3)) clone algebra.Assoc with type t = s, function op = union, goal Assoc ... ...
 ... ... @@ -51,18 +51,18 @@ theory CauchySchwarzInequality forall x y:real. y <> 0.0 -> (x/y)*y = x lemma p_val_part: forall x1 x2 y1 y2 t:real. forall x1 x2 y1 y2:real. norm2 y1 y2 > 0.0 -> p x1 x2 y1 y2 (- dot x1 x2 y1 y2 / norm2 y1 y2) = norm2 x1 x2 - sqr (dot x1 x2 y1 y2) / norm2 y1 y2 lemma p_val_part_pos: forall x1 x2 y1 y2 t:real. forall x1 x2 y1 y2:real. norm2 y1 y2 > 0.0 -> norm2 x1 x2 - sqr (dot x1 x2 y1 y2) / norm2 y1 y2 >= 0.0 lemma p_val_part_pos_aux: forall x1 x2 y1 y2 t:real. forall x1 x2 y1 y2:real. norm2 y1 y2 > 0.0 -> norm2 y1 y2 * p x1 x2 y1 y2 (- dot x1 x2 y1 y2 / norm2 y1 y2) >= 0.0 ... ...
 ... ... @@ -57,7 +57,7 @@ theory IntPathWeight end lemma path_weight_right_extension: forall x y z: vertex, l: list vertex. forall x y: vertex, l: list vertex. path_weight (l ++ Cons x Nil) y = path_weight l x + weight x y lemma path_weight_decomposition: ... ...
 ... ... @@ -135,7 +135,7 @@ theory Gcd use int.EuclideanDivision lemma Gcd_euclidean_mod: forall a b g: int [gcd b (EuclideanDivision.mod a b)]. forall a b: int [gcd b (EuclideanDivision.mod a b)]. b <> 0 -> gcd b (EuclideanDivision.mod a b) = gcd a b lemma gcd_mult: forall a b c: int. 0 <= c -> gcd (c * a) (c * b) = c * gcd a b ... ...
 ... ... @@ -111,7 +111,7 @@ theory FromInt axiom Mul: forall x y:int. from_int (Int.(*) x y) = from_int x * from_int y axiom Neg: forall x y:int. from_int (Int.(-_) (x)) = - from_int x forall x:int. from_int (Int.(-_) (x)) = - from_int x end ... ...
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