- some renaming according to the written version of 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 cf1c5d95f77b94d4112a88ceae7094d6c62272b7..0675804ccdf2295648c7a80da8103ae710802a44 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cpcs.ma
@@ -23,7 +23,7 @@ include "basic_2/equivalence/cpcs_cprs.ma".
 lemma cpcs_inv_cprs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 →
                      ∃∃T. ⦃G, L⦄ ⊢ T1 ➡* T & ⦃G, L⦄ ⊢ T2 ➡* T.
 #G #L #T1 #T2 #H @(cpcs_ind … H) -T2
-[ /3 width=3/
+[ /3 width=3 by ex2_intro/
 | #T #T2 #_ #HT2 * #T0 #HT10 elim HT2 -HT2 #HT2 #HT0
   [ elim (cprs_strip … HT0 … HT2) -T /3 width=3 by cprs_strap1, ex2_intro/
   | /3 width=5 by cprs_strap2, ex2_intro/
@@ -59,14 +59,14 @@ 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 ≡ U2 →
+lemma cpcs_inv_lift: ∀G,L,K,s,l,m. ⬇[s, l, m] L ≡ K →
+                     â\88\80T1,U1. â¬\86[l, m] T1 â\89¡ U1 â\86\92 â\88\80T2,U2. â¬\86[l, m] T2 ≡ 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 #s #l #m #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 -m /2 width=3 by cprs_div/
 qed-.
 
 (* Advanced properties ******************************************************)
@@ -106,9 +106,12 @@ qed-.
 
 (* Basic_1: was: pc3_wcpr0_t *)
 (* Basic_1: note: pc3_wcpr0_t should be renamed *)
+(* Note: alternative proof /3 width=5 by lprs_cprs_conf, lpr_lprs/ *)
 lemma lpr_cprs_conf: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 →
                      ∀T1,T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
-/3 width=5 by lprs_cprs_conf, lpr_lprs/ qed-.
+#G #L1 #L2 #HL12 #T1 #T2 #HT12 elim (cprs_lpr_conf_dx … HT12 … HL12) -L1
+/2 width=3 by cprs_div/
+qed-.
 
 (* Basic_1: was only: pc3_pr0_pr2_t *)
 (* Basic_1: note: pc3_pr0_pr2_t should be renamed *)
@@ -141,18 +144,18 @@ lemma cpcs_bind_sn: ∀a,I,G,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ⬌* V2 → ⦃G, L⦄
 qed.
 
 lemma lsubr_cpcs_trans: ∀G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬌* T2 →
-                        â\88\80L2. L2 â\8a\91 L1 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
+                        â\88\80L2. L2 â«\83 L1 → ⦃G, L2⦄ ⊢ T1 ⬌* T2.
 #G #L1 #T1 #T2 #HT12 elim (cpcs_inv_cprs … HT12) -HT12
 /3 width=5 by cprs_div, lsubr_cprs_trans/
 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 ≡ U2 →
+lemma cpcs_lift: ∀G,L,K,s,l,m. ⬇[s, l, m] L ≡ K →
+                 â\88\80T1,U1. â¬\86[l, m] T1 â\89¡ U1 â\86\92 â\88\80T2,U2. â¬\86[l, m] T2 ≡ 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 #s #l #m #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 m) /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 →
@@ -161,6 +164,7 @@ lemma cpcs_strip: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ⬌* T1 → ∀T2. ⦃G, L⦄ 
 
 (* More inversion lemmas ****************************************************)
 
+(* Note: there must be a proof suitable for llpr *)
 lemma cpcs_inv_abst_sn: ∀a1,a2,G,L,W1,W2,T1,T2. ⦃G, L⦄ ⊢ ⓛ{a1}W1.T1 ⬌* ⓛ{a2}W2.T2 →
                         ∧∧ ⦃G, L⦄ ⊢ W1 ⬌* W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬌* T2 & a1 = a2.
 #a1 #a2 #G #L #W1 #W2 #T1 #T2 #H