- notational change for cpg and cpx

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lift.ma
index 9ff2b6f2c196fd21b651243fb9070f15990f5241..9b4822e585ab4b6bff4320118775dbd6ad1eae95 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lift.ma
@@ -21,8 +21,8 @@ include "basic_2/computation/cpxs.ma".
 (* Advanced properties ******************************************************)
 
 lemma cpxs_delta: ∀h,o,I,G,L,K,V,V2,i.
-                  â¬\87[i] L â\89¡ K.â\93\91{I}V â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â\9e¡*[h, o] V2 →
-                  â\88\80W2. â¬\86[0, i+1] V2 â\89¡ W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡*[h, o] W2.
+                  â¬\87[i] L â\89¡ K.â\93\91{I}V â\86\92 â¦\83G, Kâ¦\84 â\8a¢ V â¬\88*[h, o] V2 →
+                  â\88\80W2. â¬\86[0, i+1] V2 â\89¡ W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88*[h, o] W2.
 #h #o #I #G #L #K #V #V2 #i #HLK #H elim H -V2
 [ /3 width=9 by cpx_cpxs, cpx_delta/
 | #V1 lapply (drop_fwd_drop2 … HLK) -HLK
@@ -31,7 +31,7 @@ lemma cpxs_delta: ∀h,o,I,G,L,K,V,V2,i.
 qed.
 
 lemma lstas_cpxs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
-                  â\88\80d1. â¦\83G, Lâ¦\84 â\8a¢ T1 â\96ª[h, o] d1 â\86\92 d2 â\89¤ d1 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡*[h, o] T2.
+                  â\88\80d1. â¦\83G, Lâ¦\84 â\8a¢ T1 â\96ª[h, o] d1 â\86\92 d2 â\89¤ d1 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h, o] T2.
 #h #o #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 //
 [ /3 width=3 by cpxs_sort, da_inv_sort/
 | #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
@@ -50,9 +50,9 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_lref1: â\88\80h,o,G,L,T2,i. â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡*[h, o] T2 →
+lemma cpxs_inv_lref1: â\88\80h,o,G,L,T2,i. â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88*[h, o] T2 →
                       T2 = #i ∨
-                      â\88\83â\88\83I,K,V1,T1. â¬\87[i] L â\89¡ K.â\93\91{I}V1 & â¦\83G, Kâ¦\84 â\8a¢ V1 â\9e¡*[h, o] T1 &
+                      â\88\83â\88\83I,K,V1,T1. â¬\87[i] L â\89¡ K.â\93\91{I}V1 & â¦\83G, Kâ¦\84 â\8a¢ V1 â¬\88*[h, o] T1 &
                                    ⬆[0, i+1] T1 ≡ T2.
 #h #o #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
 #T #T2 #_ #HT2 *
@@ -77,17 +77,17 @@ qed-.
 
 (* Properties on supclosure *************************************************)
 
-lemma fqu_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 →
+lemma fqu_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 →
                       ∀T1. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
+                      â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqu_cpx_trans … HT1 … HT2) -T
 #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fquq_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 →
+lemma fquq_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 →
                        ∀T1. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fquq_inv_gen … H) -H
 [ #HT12 elim (fqu_cpxs_trans … HTU2 … HT12) /3 width=3 by fqu_fquq, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
@@ -97,20 +97,20 @@ qed-.
 lemma fquq_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
                         ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
                         ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
-                        â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+                        â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
 /3 width=5 by fquq_cpxs_trans, lstas_cpxs/ qed-.
 
-lemma fqup_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 →
+lemma fqup_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 →
                        ∀T1. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
+                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqup_cpx_trans … HT1 … HT2) -T
 #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fqus_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â\9e¡*[h, o] U2 →
+lemma fqus_cpxs_trans: â\88\80h,o,G1,G2,L1,L2,T2,U2. â¦\83G2, L2â¦\84 â\8a¢ T2 â¬\88*[h, o] U2 →
                        ∀T1. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+                       â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
 #h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fqus_inv_gen … H) -H
 [ #HT12 elim (fqup_cpxs_trans … HTU2 … HT12) /3 width=3 by fqup_fqus, ex2_intro/
 | * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
@@ -120,5 +120,5 @@ qed-.
 lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
                         ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
                         ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
-                        â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+                        â\88\83â\88\83U1. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
 /3 width=6 by fqus_cpxs_trans, lstas_cpxs/ qed-.