update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_equivalence / cpcs_cprs.ma

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 bd40f01c3553147e817b5ed18d0b80e8c351bbc1..90fd0231372ba45ccfb34a2eae16335d4b5863f5 100644 (file)
--- 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): â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2 →
-                                 â\88\83â\88\83T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[h] T & â¦\83G,Lâ¦\84 ⊢ T2 ➡*[h] T.
+lemma cpcs_inv_cprs (h) (G) (L): â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T2 →
+                                 â\88\83â\88\83T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h] T & â\9dªG,Lâ\9d« ⊢ 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): â\88\80s1,s2. â¦\83G,Lâ¦\84 ⊢ ⋆s1 ⬌*[h] ⋆s2 → s1 = s2.
+lemma cpcs_inv_sort_bi (h) (G) (L): â\88\80s1,s2. â\9dªG,Lâ\9d« ⊢ ⋆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):
-                       â\88\80p,W1,T1,X. â¦\83G,Lâ¦\84 â\8a¢ â\93\9b{p}W1.T1 ⬌*[h] X →
-                       â\88\83â\88\83W2,T2. â¦\83G,Lâ¦\84 â\8a¢ X â\9e¡*[h] â\93\9b{p}W2.T2 & â¦\83G,Lâ¦\84 â\8a¢ â\93\9b{p}W1.T1 â\9e¡*[h] â\93\9b{p}W2.T2.
+                       â\88\80p,W1,T1,X. â\9dªG,Lâ\9d« â\8a¢ â\93\9b[p]W1.T1 ⬌*[h] X →
+                       â\88\83â\88\83W2,T2. â\9dªG,Lâ\9d« â\8a¢ X â\9e¡*[h] â\93\9b[p]W2.T2 & â\9dªG,Lâ\9d« â\8a¢ â\93\9b[p]W1.T1 â\9e¡*[h] â\93\9b[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):
-                       â\88\80p,W1,T1,X. â¦\83G,Lâ¦\84 â\8a¢ X â¬\8c*[h] â\93\9b{p}W1.T1 →
-                       â\88\83â\88\83W2,T2. â¦\83G,Lâ¦\84 â\8a¢ X â\9e¡*[h] â\93\9b{p}W2.T2 & â¦\83G,Lâ¦\84 â\8a¢ â\93\9b{p}W1.T1 â\9e¡*[h] â\93\9b{p}W2.T2.
+                       â\88\80p,W1,T1,X. â\9dªG,Lâ\9d« â\8a¢ X â¬\8c*[h] â\93\9b[p]W1.T1 →
+                       â\88\83â\88\83W2,T2. â\9dªG,Lâ\9d« â\8a¢ X â\9e¡*[h] â\93\9b[p]W2.T2 & â\9dªG,Lâ\9d« â\8a¢ â\93\9b[p]W1.T1 â\9e¡*[h] â\93\9b[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):
-                         â\88\80p,W,T,s. â¦\83G,Lâ¦\84 â\8a¢ â\8b\86s â¬\8c*[h] â\93\9b{p}W.T → ⊥.
+                         â\88\80p,W,T,s. â\9dªG,Lâ\9d« â\8a¢ â\8b\86s â¬\8c*[h] â\93\9b[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): â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpcs_cprs_dx (h) (G) (L): â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T2 â\9e¡*[h] T1 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpcs_cprs_sn (h) (G) (L): â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T2 â\9e¡*[h] T1 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T →
-                                     â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpcs_cprs_step_dx (h) (G) (L): â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T →
+                                     â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[h] T →
-                                     â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T â¬\8c*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpcs_cprs_step_sn (h) (G) (L): â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h] T →
+                                     â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â¬\8c*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T →
-                                 â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T2 â\9e¡*[h] T â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpcs_cprs_div (h) (G) (L): â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T →
+                                 â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T2 â\9e¡*[h] T â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T1,T. â¦\83G,Lâ¦\84 ⊢ T ➡*[h] T1 →
-                                  â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T â¬\8c*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpcs_cprs_conf (h) (G) (L): â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T ➡*[h] T1 →
+                                  â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â¬\8c*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[h] T →
-                            â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T2 â\9e¡*[h] T â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cprs_div (h) (G) (L): â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h] T →
+                            â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T2 â\9e¡*[h] T â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ➡*[h] T →
-                                â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T2 â\9e¡[h] T â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cprs_cpr_div (h) (G) (L): â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h] T →
+                                â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T2 â\9e¡[h] T â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T2.
 /3 width=5 by cpm_cpms, cprs_div/ qed-.
 
-lemma cpr_cprs_div (h) (G) (L): â\88\80T1,T. â¦\83G,Lâ¦\84 ⊢ T1 ➡[h] T →
-                                â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T2 â\9e¡*[h] T â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpr_cprs_div (h) (G) (L): â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡[h] T →
+                                â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T2 â\9e¡*[h] T â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T2.
 /3 width=3 by cpm_cpms, cprs_div/ qed-.
 
-lemma cpr_cprs_conf_cpcs (h) (G) (L): â\88\80T,T1. â¦\83G,Lâ¦\84 ⊢ T ➡*[h] T1 →
-                                      â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cpr_cprs_conf_cpcs (h) (G) (L): â\88\80T,T1. â\9dªG,Lâ\9d« ⊢ T ➡*[h] T1 →
+                                      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T,T1. â¦\83G,Lâ¦\84 ⊢ T ➡*[h] T1 →
-                                      â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T2 ⬌*[h] T1.
+lemma cprs_cpr_conf_cpcs (h) (G) (L): â\88\80T,T1. â\9dªG,Lâ\9d« ⊢ T ➡*[h] T1 →
+                                      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80T,T1. â¦\83G,Lâ¦\84 ⊢ T ➡*[h] T1 →
-                                  â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T â\9e¡*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2.
+lemma cprs_conf_cpcs (h) (G) (L): â\88\80T,T1. â\9dªG,Lâ\9d« ⊢ T ➡*[h] T1 →
+                                  â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ 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): â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V1 ⬌*[h] V2 →
-                             â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2 →
-                             â\88\80I. â¦\83G,Lâ¦\84 â\8a¢ â\93\95{I}V1.T1 â¬\8c*[h] â\93\95{I}V2.T2.
+lemma cpcs_flat (h) (G) (L): â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬌*[h] V2 →
+                             â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T2 →
+                             â\88\80I. â\9dªG,Lâ\9d« â\8a¢ â\93\95[I]V1.T1 â¬\8c*[h] â\93\95[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): â\88\80V1,V2. â¦\83G,Lâ¦\84 ⊢ V2 ➡[h] V1 →
-                                        â\88\80T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h] T2 →
-                                        â\88\80I. â¦\83G,Lâ¦\84 â\8a¢ â\93\95{I}V1.T1 â¬\8c*[h] â\93\95{I}V2.T2.
+lemma cpcs_flat_dx_cpr_rev (h) (G) (L): â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V2 ➡[h] V1 →
+                                        â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h] T2 →
+                                        â\88\80I. â\9dªG,Lâ\9d« â\8a¢ â\93\95[I]V1.T1 â¬\8c*[h] â\93\95[I]V2.T2.
 /3 width=1 by cpr_cpcs_sn, cpcs_flat/ qed.
 
-lemma cpcs_bind_dx (h) (G) (L): â\88\80I,V,T1,T2. â¦\83G,L.â\93\91{I}Vâ¦\84 ⊢ T1 ⬌*[h] T2 →
-                                â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V.T1 â¬\8c*[h] â\93\91{p,I}V.T2.
+lemma cpcs_bind_dx (h) (G) (L): â\88\80I,V,T1,T2. â\9dªG,L.â\93\91[I]Vâ\9d« ⊢ T1 ⬌*[h] T2 →
+                                â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V.T1 â¬\8c*[h] â\93\91[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): â\88\80I,V1,V2,T. â¦\83G,Lâ¦\84 ⊢ V1 ⬌*[h] V2 →
-                                â\88\80p. â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V1.T â¬\8c*[h] â\93\91{p,I}V2.T.
+lemma cpcs_bind_sn (h) (G) (L): â\88\80I,V1,V2,T. â\9dªG,Lâ\9d« ⊢ V1 ⬌*[h] V2 →
+                                â\88\80p. â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V1.T â¬\8c*[h] â\93\91[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.