X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcsx_aaa.ma;h=c963c06a4c69d4dead9b268bd6f278ee577faca2;hp=dfbcf7e487e76635ecf64acd42010ef56c7ebc45;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma index dfbcf7e48..c963c06a4 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_aaa.ma @@ -21,7 +21,7 @@ include "basic_2/rt_computation/csx_gcr.ma". (* Main properties with atomic arity assignment *****************************) -theorem aaa_csx: ∀h,G,L,T,A. ⦃G,L⦄ ⊢ T ⁝ A → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄. +theorem aaa_csx: ∀h,G,L,T,A. ❪G,L❫ ⊢ T ⁝ A → ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫. #h #G #L #T #A #H @(gcr_aaa … (csx_gcp h) (csx_gcr h) … H) qed. @@ -29,32 +29,32 @@ qed. (* Advanced eliminators *****************************************************) fact aaa_ind_csx_aux: ∀h,G,L,A. ∀Q:predicate term. - (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A → - (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 + (∀T1. ❪G,L❫ ⊢ T1 ⁝ A → + (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 ) → - ∀T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ T ⁝ A → Q T. + ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L❫ ⊢ T ⁝ A → Q T. #h #G #L #A #Q #IH #T #H @(csx_ind … H) -T /4 width=5 by cpx_aaa_conf/ qed-. lemma aaa_ind_csx: ∀h,G,L,A. ∀Q:predicate term. - (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A → - (∀T2. ⦃G,L⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 + (∀T1. ❪G,L❫ ⊢ T1 ⁝ A → + (∀T2. ❪G,L❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 ) → - ∀T. ⦃G,L⦄ ⊢ T ⁝ A → Q T. + ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T. /5 width=9 by aaa_ind_csx_aux, aaa_csx/ qed-. fact aaa_ind_csx_cpxs_aux: ∀h,G,L,A. ∀Q:predicate term. - (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A → - (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 + (∀T1. ❪G,L❫ ⊢ T1 ⁝ A → + (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 ) → - ∀T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ T ⁝ A → Q T. + ∀T. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ → ❪G,L❫ ⊢ T ⁝ A → Q T. #h #G #L #A #Q #IH #T #H @(csx_ind_cpxs … H) -T /4 width=5 by cpxs_aaa_conf/ qed-. (* Basic_2A1: was: aaa_ind_csx_alt *) lemma aaa_ind_csx_cpxs: ∀h,G,L,A. ∀Q:predicate term. - (∀T1. ⦃G,L⦄ ⊢ T1 ⁝ A → - (∀T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 + (∀T1. ❪G,L❫ ⊢ T1 ⁝ A → + (∀T2. ❪G,L❫ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1 ) → - ∀T. ⦃G,L⦄ ⊢ T ⁝ A → Q T. + ∀T. ❪G,L❫ ⊢ T ⁝ A → Q T. /5 width=9 by aaa_ind_csx_cpxs_aux, aaa_csx/ qed-.