update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / equivalence / cpcs_cpcs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
index fcf4a7ee24a6717f12e9eb69b437e7dc6a787e29..7b9645afa39f8f845e6c8c52cb368ba9363e4a77 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
@@ -32,8 +32,8 @@ lemma cpcs_inv_cprs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
 qed-.
 
 (* Basic_1: was: pc3_gen_sort *)
-lemma cpcs_inv_sort: ∀G,L,k1,k2. ⦃G, L⦄ ⊢ ⋆k1 ⬌* ⋆k2 → k1 = k2.
-#G #L #k1 #k2 #H elim (cpcs_inv_cprs … H) -H
+lemma cpcs_inv_sort: ∀G,L,s1,s2. ⦃G, L⦄ ⊢ ⋆s1 ⬌* ⋆s2 → s1 = s2.
+#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 //
 qed-.
@@ -51,22 +51,22 @@ lemma cpcs_inv_abst2: ∀a,G,L,W1,T1,T. ⦃G, L⦄ ⊢ T ⬌* ⓛ{a}W1.T1 →
 /3 width=1 by cpcs_inv_abst1, cpcs_sym/ qed-.
 
 (* Basic_1: was: pc3_gen_sort_abst *)
-lemma cpcs_inv_sort_abst: ∀a,G,L,W,T,k. ⦃G, L⦄ ⊢ ⋆k ⬌* ⓛ{a}W.T → ⊥.
-#a #G #L #W #T #k #H
+lemma cpcs_inv_sort_abst: ∀a,G,L,W,T,s. ⦃G, L⦄ ⊢ ⋆s ⬌* ⓛ{a}W.T → ⊥.
+#a #G #L #W #T #s #H
 elim (cpcs_inv_cprs … H) -H #X #H1
 >(cprs_inv_sort1 … H1) -X #H2
 elim (cprs_inv_abst1 … H2) -H2 #W0 #T0 #_ #_ #H destruct
 qed-.
 
 (* Basic_1: was: pc3_gen_lift *)
-lemma cpcs_inv_lift: ∀G,L,K,s,d,e. ⇩[s, d, e] L ≡ K →
-                     â\88\80T1,U1. â\87§[d, e] T1 â\89¡ U1 â\86\92 â\88\80T2,U2. â\87§[d, e] T2 â\89¡ U2 →
+lemma cpcs_inv_lift: ∀G,L,K,b,l,k. ⬇[b, l, k] L ≘ K →
+                     â\88\80T1,U1. â¬\86[l, k] T1 â\89\98 U1 â\86\92 â\88\80T2,U2. â¬\86[l, k] T2 â\89\98 U2 →
                      ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, K⦄ ⊢ T1 ⬌* T2.
-#G #L #K #s #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12
+#G #L #K #b #l #k #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HU12
 elim (cpcs_inv_cprs … HU12) -HU12 #U #HU1 #HU2
 elim (cprs_inv_lift1 … HU1 … HLK … HTU1) -U1 #T #HTU #HT1
 elim (cprs_inv_lift1 … HU2 … HLK … HTU2) -L -U2 #X #HXU
->(lift_inj … HXU … HTU) -X -U -d -e /2 width=3 by cprs_div/
+>(lift_inj … HXU … HTU) -X -U -l -k /2 width=3 by cprs_div/
 qed-.
 
 (* Advanced properties ******************************************************)
@@ -150,12 +150,12 @@ lemma lsubr_cpcs_trans: ∀G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬌* T2 →
 qed-.
 
 (* Basic_1: was: pc3_lift *)
-lemma cpcs_lift: ∀G,L,K,s,d,e. ⇩[s, d, e] L ≡ K →
-                 â\88\80T1,U1. â\87§[d, e] T1 â\89¡ U1 â\86\92 â\88\80T2,U2. â\87§[d, e] T2 â\89¡ U2 →
+lemma cpcs_lift: ∀G,L,K,b,l,k. ⬇[b, l, k] L ≘ K →
+                 â\88\80T1,U1. â¬\86[l, k] T1 â\89\98 U1 â\86\92 â\88\80T2,U2. â¬\86[l, k] T2 â\89\98 U2 →
                  ⦃G, K⦄ ⊢ T1 ⬌* T2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
-#G #L #K #s #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
+#G #L #K #b #l #k #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #HT12
 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
-elim (lift_total T d e) /3 width=12 by cprs_div, cprs_lift/
+elim (lift_total T l k) /3 width=12 by cprs_div, cprs_lift/
 qed.
 
 lemma cpcs_strip: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ⬌* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌ T2 →