update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / rpx_reqx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_reqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_reqx.ma
index 61b24fdae03d8bf440c33ca30ae7eb9aae45d6b7..725ddde9a56ba63a4d886d8bc503af3cb1353dbe 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_reqx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_reqx.ma
@@ -21,27 +21,27 @@ include "basic_2/rt_transition/rpx_fsle.ma".
 
 (* Properties with sort-irrelevant equivalence for local environments *******)
 
-lemma rpx_pair_sn_split: â\88\80h,G,L1,L2,V. â¦\83G,L1â¦\84 ⊢ ⬈[h,V] L2 → ∀I,T.
-                         â\88\83â\88\83L. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\91¡{I}V.T] L & L ≛[V] L2.
+lemma rpx_pair_sn_split: â\88\80h,G,L1,L2,V. â\9dªG,L1â\9d« ⊢ ⬈[h,V] L2 → ∀I,T.
+                         â\88\83â\88\83L. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\91¡[I]V.T] L & L ≛[V] L2.
 /3 width=5 by rpx_fsge_comp, rex_pair_sn_split/ qed-.
 
-lemma rpx_flat_dx_split: â\88\80h,G,L1,L2,T. â¦\83G,L1â¦\84 ⊢ ⬈[h,T] L2 → ∀I,V.
-                         â\88\83â\88\83L. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\93\95{I}V.T] L & L ≛[T] L2.
+lemma rpx_flat_dx_split: â\88\80h,G,L1,L2,T. â\9dªG,L1â\9d« ⊢ ⬈[h,T] L2 → ∀I,V.
+                         â\88\83â\88\83L. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\93\95[I]V.T] L & L ≛[T] L2.
 /3 width=5 by rpx_fsge_comp, rex_flat_dx_split/ qed-.
 
-lemma rpx_bind_dx_split: â\88\80h,I,G,L1,L2,V1,T. â¦\83G,L1.â\93\91{I}V1â¦\84 ⊢ ⬈[h,T] L2 → ∀p.
-                         â\88\83â\88\83L,V. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,â\93\91{p,I}V1.T] L & L.â\93\91{I}V â\89\9b[T] L2 & â¦\83G,L1â¦\84 ⊢ V1 ⬈[h] V.
+lemma rpx_bind_dx_split: â\88\80h,I,G,L1,L2,V1,T. â\9dªG,L1.â\93\91[I]V1â\9d« ⊢ ⬈[h,T] L2 → ∀p.
+                         â\88\83â\88\83L,V. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,â\93\91[p,I]V1.T] L & L.â\93\91[I]V â\89\9b[T] L2 & â\9dªG,L1â\9d« ⊢ V1 ⬈[h] V.
 /3 width=5 by rpx_fsge_comp, rex_bind_dx_split/ qed-.
 
-lemma rpx_bind_dx_split_void: â\88\80h,G,K1,L2,T. â¦\83G,K1.â\93§â¦\84 ⊢ ⬈[h,T] L2 → ∀p,I,V.
-                              â\88\83â\88\83K2. â¦\83G,K1â¦\84 â\8a¢ â¬\88[h,â\93\91{p,I}V.T] K2 & K2.ⓧ ≛[T] L2.
+lemma rpx_bind_dx_split_void: â\88\80h,G,K1,L2,T. â\9dªG,K1.â\93§â\9d« ⊢ ⬈[h,T] L2 → ∀p,I,V.
+                              â\88\83â\88\83K2. â\9dªG,K1â\9d« â\8a¢ â¬\88[h,â\93\91[p,I]V.T] K2 & K2.ⓧ ≛[T] L2.
 /3 width=5 by rpx_fsge_comp, rex_bind_dx_split_void/ qed-.
 
 lemma rpx_teqx_conf: ∀h,G. s_r_confluent1 … cdeq (rpx h G).
 /2 width=5 by teqx_rex_conf/ qed-.
 
 lemma rpx_teqx_div: ∀h,T1,T2. T1 ≛ T2 →
-                    â\88\80G,L1,L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h,T2] L2 â\86\92 â¦\83G,L1â¦\84 ⊢ ⬈[h,T1] L2.
+                    â\88\80G,L1,L2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h,T2] L2 â\86\92 â\9dªG,L1â\9d« ⊢ ⬈[h,T1] L2.
 /2 width=5 by teqx_rex_div/ qed-.
 
 lemma cpx_teqx_conf_rex: ∀h,G. R_confluent2_rex … (cpx h G) cdeq (cpx h G) cdeq.
@@ -125,25 +125,25 @@ lemma cpx_teqx_conf_rex: ∀h,G. R_confluent2_rex … (cpx h G) cdeq (cpx h G) c
 ]
 qed-.
 
-lemma cpx_teqx_conf: â\88\80h,G,L. â\88\80T0:term. â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T0 ⬈[h] T1 →
+lemma cpx_teqx_conf: â\88\80h,G,L. â\88\80T0:term. â\88\80T1. â\9dªG,Lâ\9d« ⊢ T0 ⬈[h] T1 →
                      ∀T2. T0 ≛ T2 →
-                     â\88\83â\88\83T. T1 â\89\9b T & â¦\83G,Lâ¦\84 ⊢ T2 ⬈[h] T.
+                     â\88\83â\88\83T. T1 â\89\9b T & â\9dªG,Lâ\9d« ⊢ T2 ⬈[h] T.
 #h #G #L #T0 #T1 #HT01 #T2 #HT02
 elim (cpx_teqx_conf_rex … HT01 … HT02 L … L) -HT01 -HT02
 /2 width=3 by rex_refl, ex2_intro/
 qed-.
 
 lemma teqx_cpx_trans: ∀h,G,L,T2. ∀T0:term. T2 ≛ T0 →
-                      â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T0 ⬈[h] T1 →
-                      â\88\83â\88\83T. â¦\83G,Lâ¦\84 ⊢ T2 ⬈[h] T & T ≛ T1.
+                      â\88\80T1. â\9dªG,Lâ\9d« ⊢ T0 ⬈[h] T1 →
+                      â\88\83â\88\83T. â\9dªG,Lâ\9d« ⊢ T2 ⬈[h] T & T ≛ T1.
 #h #G #L #T2 #T0 #HT20 #T1 #HT01
 elim (cpx_teqx_conf … HT01 T2) -HT01 /3 width=3 by teqx_sym, ex2_intro/
 qed-.
 
 (* Basic_2A1: uses: cpx_lleq_conf *)
-lemma cpx_reqx_conf: â\88\80h,G,L0,T0,T1. â¦\83G,L0â¦\84 ⊢ T0 ⬈[h] T1 →
+lemma cpx_reqx_conf: â\88\80h,G,L0,T0,T1. â\9dªG,L0â\9d« ⊢ T0 ⬈[h] T1 →
                      ∀L2. L0 ≛[T0] L2 →
-                     â\88\83â\88\83T. â¦\83G,L2â¦\84 ⊢ T0 ⬈[h] T & T1 ≛ T.
+                     â\88\83â\88\83T. â\9dªG,L2â\9d« ⊢ T0 ⬈[h] T & T1 ≛ T.
 #h #G #L0 #T0 #T1 #HT01 #L2 #HL02
 elim (cpx_teqx_conf_rex … HT01 T0 … L0 … HL02) -HT01 -HL02
 /2 width=3 by rex_refl, ex2_intro/
@@ -151,8 +151,8 @@ qed-.
 
 (* Basic_2A1: uses: lleq_cpx_trans *)
 lemma reqx_cpx_trans: ∀h,G,L2,L0,T0. L2 ≛[T0] L0 →
-                      â\88\80T1. â¦\83G,L0â¦\84 ⊢ T0 ⬈[h] T1 →
-                      â\88\83â\88\83T. â¦\83G,L2â¦\84 ⊢ T0 ⬈[h] T & T ≛ T1.
+                      â\88\80T1. â\9dªG,L0â\9d« ⊢ T0 ⬈[h] T1 →
+                      â\88\83â\88\83T. â\9dªG,L2â\9d« ⊢ T0 ⬈[h] T & T ≛ T1.
 #h #G #L2 #L0 #T0 #HL20 #T1 #HT01
 elim (cpx_reqx_conf … HT01 L2) -HT01
 /3 width=3 by reqx_sym, teqx_sym, ex2_intro/
@@ -161,9 +161,9 @@ qed-.
 lemma rpx_reqx_conf: ∀h,G,T. confluent2 … (rpx h G T) (reqx T).
 /3 width=6 by rpx_fsge_comp, reqx_fsge_comp, cpx_teqx_conf_rex, rex_conf/ qed-.
 
-lemma reqx_rpx_trans: â\88\80h,G,T,L2,K2. â¦\83G,L2â¦\84 ⊢ ⬈[h,T] K2 →
+lemma reqx_rpx_trans: â\88\80h,G,T,L2,K2. â\9dªG,L2â\9d« ⊢ ⬈[h,T] K2 →
                       ∀L1. L1 ≛[T] L2 →
-                      â\88\83â\88\83K1. â¦\83G,L1â¦\84 ⊢ ⬈[h,T] K1 & K1 ≛[T] K2.
+                      â\88\83â\88\83K1. â\9dªG,L1â\9d« ⊢ ⬈[h,T] K1 & K1 ≛[T] K2.
 #h #G #T #L2 #K2 #HLK2 #L1 #HL12
 elim (rpx_reqx_conf … HLK2 L1)
 /3 width=3 by reqx_sym, ex2_intro/