X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FLambdaDelta-1%2Ftlt%2Fprops.ma;h=72b13d733f8628b6a33c31dac064244daa8f3a60;hb=f5dfc6c24a393a4717a7b40689df768d271d9ac0;hp=56f46e4eae286831af1e6769628ac8386de984b2;hpb=d0982534aee06a30f91a06d2f3e82834b132a3d3;p=helm.git diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/tlt/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/tlt/props.ma index 56f46e4ea..72b13d733 100644 --- a/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/tlt/props.ma +++ b/helm/software/matita/contribs/LAMBDA-TYPES/LambdaDelta-1/tlt/props.ma @@ -14,7 +14,7 @@ (* This file was automatically generated: do not edit *********************) -include "tlt/defs.ma". +include "LambdaDelta-1/tlt/defs.ma". theorem wadd_le: \forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: @@ -88,7 +88,7 @@ t1))))))).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le (f n) (g n))))).(le_n_S (plus (weight_map f t0) (weight_map (wadd f (S (weight_map f t0))) t1)) (plus (weight_map g t0) (weight_map (wadd g (S (weight_map g t0))) t1)) -(plus_le_compat (weight_map f t0) (weight_map g t0) (weight_map (wadd f (S +(le_plus_plus (weight_map f t0) (weight_map g t0) (weight_map (wadd f (S (weight_map f t0))) t1) (weight_map (wadd g (S (weight_map g t0))) t1) (H f g H1) (H0 (wadd f (S (weight_map f t0))) (wadd g (S (weight_map g t0))) (\lambda (n: nat).(wadd_le f g H1 (S (weight_map f t0)) (S (weight_map g t0)) @@ -100,31 +100,30 @@ t0) (weight_map g t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f: (g n)))) \to (le (weight_map f t1) (weight_map g t1))))))).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le (f n) (g n))))).(le_n_S (plus (weight_map f t0) (weight_map (wadd f O) t1)) -(plus (weight_map g t0) (weight_map (wadd g O) t1)) (plus_le_compat -(weight_map f t0) (weight_map g t0) (weight_map (wadd f O) t1) (weight_map -(wadd g O) t1) (H f g H1) (H0 (wadd f O) (wadd g O) (\lambda (n: -nat).(wadd_le f g H1 O O (le_n O) n)))))))))))) (\lambda (t0: T).(\lambda (H: -((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: -nat).(le (f n) (g n)))) \to (le (weight_map f t0) (weight_map g -t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f: ((nat \to +(plus (weight_map g t0) (weight_map (wadd g O) t1)) (le_plus_plus (weight_map +f t0) (weight_map g t0) (weight_map (wadd f O) t1) (weight_map (wadd g O) t1) +(H f g H1) (H0 (wadd f O) (wadd g O) (\lambda (n: nat).(wadd_le f g H1 O O +(le_n O) n)))))))))))) (\lambda (t0: T).(\lambda (H: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f n) (g n)))) -\to (le (weight_map f t1) (weight_map g t1))))))).(\lambda (f: ((nat \to -nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le (f -n) (g n))))).(le_n_S (plus (weight_map f t0) (weight_map (wadd f O) t1)) -(plus (weight_map g t0) (weight_map (wadd g O) t1)) (plus_le_compat -(weight_map f t0) (weight_map g t0) (weight_map (wadd f O) t1) (weight_map -(wadd g O) t1) (H f g H1) (H0 (wadd f O) (wadd g O) (\lambda (n: -nat).(wadd_le f g H1 O O (le_n O) n)))))))))))) b)) (\lambda (_: F).(\lambda -(t0: T).(\lambda (H: ((\forall (f0: ((nat \to nat))).(\forall (g: ((nat \to -nat))).(((\forall (n: nat).(le (f0 n) (g n)))) \to (le (weight_map f0 t0) -(weight_map g t0))))))).(\lambda (t1: T).(\lambda (H0: ((\forall (f0: ((nat -\to nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f0 n) (g -n)))) \to (le (weight_map f0 t1) (weight_map g t1))))))).(\lambda (f0: ((nat -\to nat))).(\lambda (g: ((nat \to nat))).(\lambda (H1: ((\forall (n: nat).(le -(f0 n) (g n))))).(le_n_S (plus (weight_map f0 t0) (weight_map f0 t1)) (plus -(weight_map g t0) (weight_map g t1)) (plus_le_compat (weight_map f0 t0) -(weight_map g t0) (weight_map f0 t1) (weight_map g t1) (H f0 g H1) (H0 f0 g -H1))))))))))) k)) t). +\to (le (weight_map f t0) (weight_map g t0))))))).(\lambda (t1: T).(\lambda +(H0: ((\forall (f: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall +(n: nat).(le (f n) (g n)))) \to (le (weight_map f t1) (weight_map g +t1))))))).(\lambda (f: ((nat \to nat))).(\lambda (g: ((nat \to +nat))).(\lambda (H1: ((\forall (n: nat).(le (f n) (g n))))).(le_n_S (plus +(weight_map f t0) (weight_map (wadd f O) t1)) (plus (weight_map g t0) +(weight_map (wadd g O) t1)) (le_plus_plus (weight_map f t0) (weight_map g t0) +(weight_map (wadd f O) t1) (weight_map (wadd g O) t1) (H f g H1) (H0 (wadd f +O) (wadd g O) (\lambda (n: nat).(wadd_le f g H1 O O (le_n O) n)))))))))))) +b)) (\lambda (_: F).(\lambda (t0: T).(\lambda (H: ((\forall (f0: ((nat \to +nat))).(\forall (g: ((nat \to nat))).(((\forall (n: nat).(le (f0 n) (g n)))) +\to (le (weight_map f0 t0) (weight_map g t0))))))).(\lambda (t1: T).(\lambda +(H0: ((\forall (f0: ((nat \to nat))).(\forall (g: ((nat \to nat))).(((\forall +(n: nat).(le (f0 n) (g n)))) \to (le (weight_map f0 t1) (weight_map g +t1))))))).(\lambda (f0: ((nat \to nat))).(\lambda (g: ((nat \to +nat))).(\lambda (H1: ((\forall (n: nat).(le (f0 n) (g n))))).(le_n_S (plus +(weight_map f0 t0) (weight_map f0 t1)) (plus (weight_map g t0) (weight_map g +t1)) (le_plus_plus (weight_map f0 t0) (weight_map g t0) (weight_map f0 t1) +(weight_map g t1) (H f0 g H1) (H0 f0 g H1))))))))))) k)) t). theorem weight_eq: \forall (t: T).(\forall (f: ((nat \to nat))).(\forall (g: ((nat \to