X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FLAMBDA-TYPES%2FBasic-1%2Fpr0%2Fsubst1.ma;h=877f87f0173178efff7dd6b792787dd45e958cf9;hb=b31c093c364e76cc6c4657008f3f259955311911;hp=0913488908021a7a7ec3189f636e7a2896378348;hpb=3531d88e2a19cba027b4b882f8dd74bf37283b9c;p=helm.git diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/pr0/subst1.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/pr0/subst1.ma index 091348890..877f87f01 100644 --- a/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/pr0/subst1.ma +++ b/helm/software/matita/contribs/LAMBDA-TYPES/Basic-1/pr0/subst1.ma @@ -14,9 +14,9 @@ (* This file was automatically generated: do not edit *********************) -include "LambdaDelta-1/pr0/props.ma". +include "Basic-1/pr0/props.ma". -include "LambdaDelta-1/subst1/defs.ma". +include "Basic-1/subst1/defs.ma". theorem pr0_delta1: \forall (u1: T).(\forall (u2: T).((pr0 u1 u2) \to (\forall (t1: T).(\forall @@ -29,6 +29,9 @@ T).(\lambda (t2: T).(\lambda (H0: (pr0 t1 t2)).(\lambda (w: T).(\lambda (H1: Abbr) u1 t1) (THead (Bind Abbr) u2 t))) (pr0_comp u1 u2 H t1 t2 H0 (Bind Abbr)) (\lambda (t0: T).(\lambda (H2: (subst0 O u2 t2 t0)).(pr0_delta u1 u2 H t1 t2 H0 t0 H2))) w H1)))))))). +(* COMMENTS +Initial nodes: 115 +END *) theorem pr0_subst1_back: \forall (u2: T).(\forall (t1: T).(\forall (t2: T).(\forall (i: nat).((subst1 @@ -47,6 +50,9 @@ T).(subst1 i u1 t1 t)) (\lambda (t: T).(pr0 t t0))) (\lambda (x: T).(\lambda (H2: (subst0 i u1 t1 x)).(\lambda (H3: (pr0 x t0)).(ex_intro2 T (\lambda (t: T).(subst1 i u1 t1 t)) (\lambda (t: T).(pr0 t t0)) x (subst1_single i u1 t1 x H2) H3)))) (pr0_subst0_back u2 t1 t0 i H0 u1 H1)))))) t2 H))))). +(* COMMENTS +Initial nodes: 251 +END *) theorem pr0_subst1_fwd: \forall (u2: T).(\forall (t1: T).(\forall (t2: T).(\forall (i: nat).((subst1 @@ -65,6 +71,9 @@ T).(subst1 i u1 t1 t)) (\lambda (t: T).(pr0 t0 t))) (\lambda (x: T).(\lambda (H2: (subst0 i u1 t1 x)).(\lambda (H3: (pr0 t0 x)).(ex_intro2 T (\lambda (t: T).(subst1 i u1 t1 t)) (\lambda (t: T).(pr0 t0 t)) x (subst1_single i u1 t1 x H2) H3)))) (pr0_subst0_fwd u2 t1 t0 i H0 u1 H1)))))) t2 H))))). +(* COMMENTS +Initial nodes: 251 +END *) theorem pr0_subst1: \forall (t1: T).(\forall (t2: T).((pr0 t1 t2) \to (\forall (v1: T).(\forall @@ -90,4 +99,7 @@ w2)) (\lambda (w2: T).(subst1 i v2 t2 w2))) (\lambda (x: T).(\lambda (H4: (pr0 t0 x)).(\lambda (H5: (subst0 i v2 t2 x)).(ex_intro2 T (\lambda (w2: T).(pr0 t0 w2)) (\lambda (w2: T).(subst1 i v2 t2 w2)) x H4 (subst1_single i v2 t2 x H5))))) H3)) (pr0_subst0 t1 t2 H v1 t0 i H1 v2 H2)))))) w1 H0))))))). +(* COMMENTS +Initial nodes: 385 +END *)