X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fex0%2Fprops.ma;h=96dd77da32096e890b34708d6eafeed56ea78c3b;hb=a4cd6a8a1d6a008518c12daca794b9e811c1dee5;hp=148879216ca30fefbabaee3675b8da399f34e3ee;hpb=3531d88e2a19cba027b4b882f8dd74bf37283b9c;p=helm.git diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/ex0/props.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/ex0/props.ma index 148879216..96dd77da3 100644 --- a/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/ex0/props.ma +++ b/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/ex0/props.ma @@ -14,11 +14,11 @@ (* This file was automatically generated: do not edit *********************) -include "LambdaDelta-1/ex0/defs.ma". +include "Basic-1/ex0/defs.ma". -include "LambdaDelta-1/leq/defs.ma". +include "Basic-1/leq/defs.ma". -include "LambdaDelta-1/aplus/props.ma". +include "Basic-1/aplus/props.ma". theorem aplus_gz_le: \forall (k: nat).(\forall (h: nat).(\forall (n: nat).((le h k) \to (eq A @@ -52,6 +52,9 @@ k0)) a)) (eq_ind A (aplus gz (asucc gz (ASort (S n) n0)) k0) (\lambda (a: A).(eq A a (aplus gz (ASort n n0) k0))) (refl_equal A (aplus gz (ASort n n0) k0)) (asucc gz (aplus gz (ASort (S n) n0) k0)) (aplus_asucc gz k0 (ASort (S n) n0))) (ASort O (plus (minus k0 n) n0)) (IH n n0 H_y))))))) h)))) k). +(* COMMENTS +Initial nodes: 683 +END *) theorem aplus_gz_ge: \forall (n: nat).(\forall (k: nat).(\forall (h: nat).((le k h) \to (eq A @@ -79,6 +82,9 @@ gz (ASort (S n0) n) k0)) a)) (eq_ind A (aplus gz (asucc gz (ASort (S n0) n)) k0) (\lambda (a: A).(eq A a (aplus gz (ASort n0 n) k0))) (refl_equal A (aplus gz (ASort n0 n) k0)) (asucc gz (aplus gz (ASort (S n0) n) k0)) (aplus_asucc gz k0 (ASort (S n0) n))) (ASort (minus n0 k0) n) (IH n0 H_y)))))) h)))) k)). +(* COMMENTS +Initial nodes: 524 +END *) theorem next_plus_gz: \forall (n: nat).(\forall (h: nat).(eq nat (next_plus gz n h) (plus h n))) @@ -87,6 +93,9 @@ theorem next_plus_gz: (next_plus gz n n0) (plus n0 n))) (refl_equal nat n) (\lambda (n0: nat).(\lambda (H: (eq nat (next_plus gz n n0) (plus n0 n))).(f_equal nat nat S (next_plus gz n n0) (plus n0 n) H))) h)). +(* COMMENTS +Initial nodes: 77 +END *) theorem leqz_leq: \forall (a1: A).(\forall (a2: A).((leq gz a1 a2) \to (leqz a1 a2))) @@ -156,6 +165,9 @@ plus) (minus k h1) n1)])) (ASort O (plus (minus k h1) n1)) (ASort O (plus A).(\lambda (_: (leq gz a0 a3)).(\lambda (H1: (leqz a0 a3)).(\lambda (a4: A).(\lambda (a5: A).(\lambda (_: (leq gz a4 a5)).(\lambda (H3: (leqz a4 a5)).(leqz_head a0 a3 H1 a4 a5 H3))))))))) a1 a2 H))). +(* COMMENTS +Initial nodes: 1375 +END *) theorem leq_leqz: \forall (a1: A).(\forall (a2: A).((leqz a1 a2) \to (leq gz a1 a2))) @@ -189,4 +201,7 @@ h2)) (aplus_asort_simpl gz (plus h1 h2) h1 n1)))))))) (\lambda (a0: A).(\lambda (a3: A).(\lambda (_: (leqz a0 a3)).(\lambda (H1: (leq gz a0 a3)).(\lambda (a4: A).(\lambda (a5: A).(\lambda (_: (leqz a4 a5)).(\lambda (H3: (leq gz a4 a5)).(leq_head gz a0 a3 H1 a4 a5 H3))))))))) a1 a2 H))). +(* COMMENTS +Initial nodes: 717 +END *)