X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_equivalence%2Fcpcs_cprs.ma;h=90fd0231372ba45ccfb34a2eae16335d4b5863f5;hp=bd40f01c3553147e817b5ed18d0b80e8c351bbc1;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_cprs.ma index bd40f01c3..90fd02313 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_cprs.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_equivalence/cpcs_cprs.ma @@ -20,8 +20,8 @@ include "basic_2/rt_equivalence/cpcs.ma". (* Inversion lemmas with context sensitive r-computation on terms ***********) -lemma cpcs_inv_cprs (h) (G) (L): ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → - ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[h] T & ⦃G,L⦄ ⊢ T2 ➡*[h] T. +lemma cpcs_inv_cprs (h) (G) (L): ∀T1,T2. ❪G,L❫ ⊢ T1 ⬌*[h] T2 → + ∃∃T. ❪G,L❫ ⊢ T1 ➡*[h] T & ❪G,L❫ ⊢ T2 ➡*[h] T. #h #G #L #T1 #T2 #H @(cpcs_ind_dx … H) -T2 [ /3 width=3 by ex2_intro/ | #T #T2 #_ #HT2 * #T0 #HT10 elim HT2 -HT2 #HT2 #HT0 @@ -35,7 +35,7 @@ qed-. (* Basic_1: was: pc3_gen_sort *) (* Basic_2A1: was: cpcs_inv_sort *) -lemma cpcs_inv_sort_bi (h) (G) (L): ∀s1,s2. ⦃G,L⦄ ⊢ ⋆s1 ⬌*[h] ⋆s2 → s1 = s2. +lemma cpcs_inv_sort_bi (h) (G) (L): ∀s1,s2. ❪G,L❫ ⊢ ⋆s1 ⬌*[h] ⋆s2 → s1 = s2. #h #G #L #s1 #s2 #H elim (cpcs_inv_cprs … H) -H #T #H1 >(cprs_inv_sort1 … H1) -T #H2 lapply (cprs_inv_sort1 … H2) -L #H destruct // @@ -43,8 +43,8 @@ qed-. (* Basic_2A1: was: cpcs_inv_abst1 *) lemma cpcs_inv_abst_sn (h) (G) (L): - ∀p,W1,T1,X. ⦃G,L⦄ ⊢ ⓛ{p}W1.T1 ⬌*[h] X → - ∃∃W2,T2. ⦃G,L⦄ ⊢ X ➡*[h] ⓛ{p}W2.T2 & ⦃G,L⦄ ⊢ ⓛ{p}W1.T1 ➡*[h] ⓛ{p}W2.T2. + ∀p,W1,T1,X. ❪G,L❫ ⊢ ⓛ[p]W1.T1 ⬌*[h] X → + ∃∃W2,T2. ❪G,L❫ ⊢ X ➡*[h] ⓛ[p]W2.T2 & ❪G,L❫ ⊢ ⓛ[p]W1.T1 ➡*[h] ⓛ[p]W2.T2. #h #G #L #p #W1 #T1 #T #H elim (cpcs_inv_cprs … H) -H #X #H1 #H2 elim (cpms_inv_abst_sn … H1) -H1 #W2 #T2 #HW12 #HT12 #H destruct @@ -53,13 +53,13 @@ qed-. (* Basic_2A1: was: cpcs_inv_abst2 *) lemma cpcs_inv_abst_dx (h) (G) (L): - ∀p,W1,T1,X. ⦃G,L⦄ ⊢ X ⬌*[h] ⓛ{p}W1.T1 → - ∃∃W2,T2. ⦃G,L⦄ ⊢ X ➡*[h] ⓛ{p}W2.T2 & ⦃G,L⦄ ⊢ ⓛ{p}W1.T1 ➡*[h] ⓛ{p}W2.T2. + ∀p,W1,T1,X. ❪G,L❫ ⊢ X ⬌*[h] ⓛ[p]W1.T1 → + ∃∃W2,T2. ❪G,L❫ ⊢ X ➡*[h] ⓛ[p]W2.T2 & ❪G,L❫ ⊢ ⓛ[p]W1.T1 ➡*[h] ⓛ[p]W2.T2. /3 width=1 by cpcs_inv_abst_sn, cpcs_sym/ qed-. (* Basic_1: was: pc3_gen_sort_abst *) lemma cpcs_inv_sort_abst (h) (G) (L): - ∀p,W,T,s. ⦃G,L⦄ ⊢ ⋆s ⬌*[h] ⓛ{p}W.T → ⊥. + ∀p,W,T,s. ❪G,L❫ ⊢ ⋆s ⬌*[h] ⓛ[p]W.T → ⊥. #h #G #L #p #W #T #s #H elim (cpcs_inv_cprs … H) -H #X #H1 >(cprs_inv_sort1 … H1) -X #H2 @@ -69,97 +69,97 @@ qed-. (* Properties with context sensitive r-computation on terms *****************) (* Basic_1: was: pc3_pr3_r *) -lemma cpcs_cprs_dx (h) (G) (L): ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpcs_cprs_dx (h) (G) (L): ∀T1,T2. ❪G,L❫ ⊢ T1 ➡*[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /3 width=3 by cpcs_cpr_step_dx, cpcs_step_dx, cpc_cpcs/ qed. (* Basic_1: was: pc3_pr3_x *) -lemma cpcs_cprs_sn (h) (G) (L): ∀T1,T2. ⦃G,L⦄ ⊢ T2 ➡*[h] T1 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpcs_cprs_sn (h) (G) (L): ∀T1,T2. ❪G,L❫ ⊢ T2 ➡*[h] T1 → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T1 #T2 #H @(cprs_ind_sn … H) -T2 /3 width=3 by cpcs_cpr_div, cpcs_step_sn, cpcs_cprs_dx/ qed. (* Basic_2A1: was: cpcs_cprs_strap1 *) -lemma cpcs_cprs_step_dx (h) (G) (L): ∀T1,T. ⦃G,L⦄ ⊢ T1 ⬌*[h] T → - ∀T2. ⦃G,L⦄ ⊢ T ➡*[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpcs_cprs_step_dx (h) (G) (L): ∀T1,T. ❪G,L❫ ⊢ T1 ⬌*[h] T → + ∀T2. ❪G,L❫ ⊢ T ➡*[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=3 by cpcs_cpr_step_dx/ qed-. (* Basic_2A1: was: cpcs_cprs_strap2 *) -lemma cpcs_cprs_step_sn (h) (G) (L): ∀T1,T. ⦃G,L⦄ ⊢ T1 ➡*[h] T → - ∀T2. ⦃G,L⦄ ⊢ T ⬌*[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpcs_cprs_step_sn (h) (G) (L): ∀T1,T. ❪G,L❫ ⊢ T1 ➡*[h] T → + ∀T2. ❪G,L❫ ⊢ T ⬌*[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T1 #T #H #T2 #HT2 @(cprs_ind_sn … H) -T1 /2 width=3 by cpcs_cpr_step_sn/ qed-. -lemma cpcs_cprs_div (h) (G) (L): ∀T1,T. ⦃G,L⦄ ⊢ T1 ⬌*[h] T → - ∀T2. ⦃G,L⦄ ⊢ T2 ➡*[h] T → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpcs_cprs_div (h) (G) (L): ∀T1,T. ❪G,L❫ ⊢ T1 ⬌*[h] T → + ∀T2. ❪G,L❫ ⊢ T2 ➡*[h] T → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T1 #T #HT1 #T2 #H @(cprs_ind_sn … H) -T2 /2 width=3 by cpcs_cpr_div/ qed-. (* Basic_1: was: pc3_pr3_conf *) -lemma cpcs_cprs_conf (h) (G) (L): ∀T1,T. ⦃G,L⦄ ⊢ T ➡*[h] T1 → - ∀T2. ⦃G,L⦄ ⊢ T ⬌*[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpcs_cprs_conf (h) (G) (L): ∀T1,T. ❪G,L❫ ⊢ T ➡*[h] T1 → + ∀T2. ❪G,L❫ ⊢ T ⬌*[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /2 width=3 by cpcs_cpr_conf/ qed-. (* Basic_1: was: pc3_pr3_t *) (* Basic_1: note: pc3_pr3_t should be renamed *) -lemma cprs_div (h) (G) (L): ∀T1,T. ⦃G,L⦄ ⊢ T1 ➡*[h] T → - ∀T2. ⦃G,L⦄ ⊢ T2 ➡*[h] T → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cprs_div (h) (G) (L): ∀T1,T. ❪G,L❫ ⊢ T1 ➡*[h] T → + ∀T2. ❪G,L❫ ⊢ T2 ➡*[h] T → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T1 #T #HT1 #T2 #H @(cprs_ind_sn … H) -T2 /2 width=3 by cpcs_cpr_div, cpcs_cprs_dx/ qed. -lemma cprs_cpr_div (h) (G) (L): ∀T1,T. ⦃G,L⦄ ⊢ T1 ➡*[h] T → - ∀T2. ⦃G,L⦄ ⊢ T2 ➡[h] T → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cprs_cpr_div (h) (G) (L): ∀T1,T. ❪G,L❫ ⊢ T1 ➡*[h] T → + ∀T2. ❪G,L❫ ⊢ T2 ➡[h] T → ❪G,L❫ ⊢ T1 ⬌*[h] T2. /3 width=5 by cpm_cpms, cprs_div/ qed-. -lemma cpr_cprs_div (h) (G) (L): ∀T1,T. ⦃G,L⦄ ⊢ T1 ➡[h] T → - ∀T2. ⦃G,L⦄ ⊢ T2 ➡*[h] T → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpr_cprs_div (h) (G) (L): ∀T1,T. ❪G,L❫ ⊢ T1 ➡[h] T → + ∀T2. ❪G,L❫ ⊢ T2 ➡*[h] T → ❪G,L❫ ⊢ T1 ⬌*[h] T2. /3 width=3 by cpm_cpms, cprs_div/ qed-. -lemma cpr_cprs_conf_cpcs (h) (G) (L): ∀T,T1. ⦃G,L⦄ ⊢ T ➡*[h] T1 → - ∀T2. ⦃G,L⦄ ⊢ T ➡[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cpr_cprs_conf_cpcs (h) (G) (L): ∀T,T1. ❪G,L❫ ⊢ T ➡*[h] T1 → + ∀T2. ❪G,L❫ ⊢ T ➡[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T #T1 #HT1 #T2 #HT2 elim (cprs_strip … HT1 … HT2) -HT1 -HT2 /2 width=3 by cpr_cprs_div/ qed-. -lemma cprs_cpr_conf_cpcs (h) (G) (L): ∀T,T1. ⦃G,L⦄ ⊢ T ➡*[h] T1 → - ∀T2. ⦃G,L⦄ ⊢ T ➡[h] T2 → ⦃G,L⦄ ⊢ T2 ⬌*[h] T1. +lemma cprs_cpr_conf_cpcs (h) (G) (L): ∀T,T1. ❪G,L❫ ⊢ T ➡*[h] T1 → + ∀T2. ❪G,L❫ ⊢ T ➡[h] T2 → ❪G,L❫ ⊢ T2 ⬌*[h] T1. #h #G #L #T #T1 #HT1 #T2 #HT2 elim (cprs_strip … HT1 … HT2) -HT1 -HT2 /2 width=3 by cprs_cpr_div/ qed-. -lemma cprs_conf_cpcs (h) (G) (L): ∀T,T1. ⦃G,L⦄ ⊢ T ➡*[h] T1 → - ∀T2. ⦃G,L⦄ ⊢ T ➡*[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2. +lemma cprs_conf_cpcs (h) (G) (L): ∀T,T1. ❪G,L❫ ⊢ T ➡*[h] T1 → + ∀T2. ❪G,L❫ ⊢ T ➡*[h] T2 → ❪G,L❫ ⊢ T1 ⬌*[h] T2. #h #G #L #T #T1 #HT1 #T2 #HT2 elim (cprs_conf … HT1 … HT2) -HT1 -HT2 /2 width=3 by cprs_div/ qed-. (* Basic_1: was only: pc3_thin_dx *) -lemma cpcs_flat (h) (G) (L): ∀V1,V2. ⦃G,L⦄ ⊢ V1 ⬌*[h] V2 → - ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → - ∀I. ⦃G,L⦄ ⊢ ⓕ{I}V1.T1 ⬌*[h] ⓕ{I}V2.T2. +lemma cpcs_flat (h) (G) (L): ∀V1,V2. ❪G,L❫ ⊢ V1 ⬌*[h] V2 → + ∀T1,T2. ❪G,L❫ ⊢ T1 ⬌*[h] T2 → + ∀I. ❪G,L❫ ⊢ ⓕ[I]V1.T1 ⬌*[h] ⓕ[I]V2.T2. #h #G #L #V1 #V2 #HV12 #T1 #T2 #HT12 elim (cpcs_inv_cprs … HV12) -HV12 elim (cpcs_inv_cprs … HT12) -HT12 /3 width=5 by cprs_flat, cprs_div/ qed. -lemma cpcs_flat_dx_cpr_rev (h) (G) (L): ∀V1,V2. ⦃G,L⦄ ⊢ V2 ➡[h] V1 → - ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → - ∀I. ⦃G,L⦄ ⊢ ⓕ{I}V1.T1 ⬌*[h] ⓕ{I}V2.T2. +lemma cpcs_flat_dx_cpr_rev (h) (G) (L): ∀V1,V2. ❪G,L❫ ⊢ V2 ➡[h] V1 → + ∀T1,T2. ❪G,L❫ ⊢ T1 ⬌*[h] T2 → + ∀I. ❪G,L❫ ⊢ ⓕ[I]V1.T1 ⬌*[h] ⓕ[I]V2.T2. /3 width=1 by cpr_cpcs_sn, cpcs_flat/ qed. -lemma cpcs_bind_dx (h) (G) (L): ∀I,V,T1,T2. ⦃G,L.ⓑ{I}V⦄ ⊢ T1 ⬌*[h] T2 → - ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V.T1 ⬌*[h] ⓑ{p,I}V.T2. +lemma cpcs_bind_dx (h) (G) (L): ∀I,V,T1,T2. ❪G,L.ⓑ[I]V❫ ⊢ T1 ⬌*[h] T2 → + ∀p. ❪G,L❫ ⊢ ⓑ[p,I]V.T1 ⬌*[h] ⓑ[p,I]V.T2. #h #G #L #I #V #T1 #T2 #HT12 elim (cpcs_inv_cprs … HT12) -HT12 /3 width=5 by cprs_div, cpms_bind/ qed. -lemma cpcs_bind_sn (h) (G) (L): ∀I,V1,V2,T. ⦃G,L⦄ ⊢ V1 ⬌*[h] V2 → - ∀p. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T ⬌*[h] ⓑ{p,I}V2.T. +lemma cpcs_bind_sn (h) (G) (L): ∀I,V1,V2,T. ❪G,L❫ ⊢ V1 ⬌*[h] V2 → + ∀p. ❪G,L❫ ⊢ ⓑ[p,I]V1.T ⬌*[h] ⓑ[p,I]V2.T. #h #G #L #I #V1 #V2 #T #HV12 elim (cpcs_inv_cprs … HV12) -HV12 /3 width=5 by cprs_div, cpms_bind/ qed.