Commit 4c831e45 authored by MARCHE Claude's avatar 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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