X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fequivalence%2Fcpcs.ma;h=75964c6159eaec418568c095317df546891f1b28;hb=e62715437a9c39244c9809c00585a5ef44a39797;hp=d26648839dc0692fbceb606f306d54ec95988526;hpb=65008df95049eb835941ffea1aa682c9253c4c2b;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
index d26648839..75964c615 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
@@ -12,79 +12,82 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/pconvstar_3.ma".
+include "basic_2/notation/relations/pconvstar_4.ma".
 include "basic_2/conversion/cpc.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
 
-definition cpcs: lenv → relation term ≝ LTC … cpc.
+definition cpcs: relation4 genv lenv term term ≝
+           λG. CTC … (cpc G).
 
 interpretation "context-sensitive parallel equivalence (term)"
-   'PConvStar L T1 T2 = (cpcs L T1 T2).
+   'PConvStar G L T1 T2 = (cpcs G L T1 T2).
 
 (* Basic eliminators ********************************************************)
 
-lemma cpcs_ind: ∀L,T1. ∀R:predicate term. R T1 →
-                (∀T,T2. L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → R T → R T2) →
-                ∀T2. L ⊢ T1 ⬌* T2 → R T2.
-#L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
+lemma cpcs_ind: ∀G,L,T1. ∀R:predicate term. R T1 →
+                (∀T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → R T → R T2) →
+                ∀T2. ⦃G, L⦄ ⊢ T1 ⬌* T2 → R T2.
+normalize /3 width=6 by TC_star_ind/
 qed-.
 
-lemma cpcs_ind_dx: ∀L,T2. ∀R:predicate term. R T2 →
-                   (∀T1,T. L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → R T → R T1) →
-                   ∀T1. L ⊢ T1 ⬌* T2 → R T1.
-#L #T2 #R #HT2 #IHT2 #T1 #HT12
-@(TC_star_ind_dx … HT2 IHT2 … HT12) //
+lemma cpcs_ind_dx: ∀G,L,T2. ∀R:predicate term. R T2 →
+                   (∀T1,T. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → R T → R T1) →
+                   ∀T1. ⦃G, L⦄ ⊢ T1 ⬌* T2 → R T1.
+normalize /3 width=6 by TC_star_ind_dx/
 qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: pc3_refl *)
-lemma cpcs_refl: ∀L. reflexive … (cpcs L).
-/2 width=1/ qed.
+lemma cpcs_refl: ∀G,L. reflexive … (cpcs G L).
+/2 width=1 by inj/ qed.
 
 (* Basic_1: was: pc3_s *)
-lemma cpcs_sym: ∀L. symmetric … (cpcs L).
-#L @TC_symmetric // qed.
+lemma cpcs_sym: ∀G,L. symmetric … (cpcs G L).
+normalize /3 width=1 by cpc_sym, TC_symmetric/
+qed-.
 
-lemma cpc_cpcs: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → L ⊢ T2 ⬌* T2.
-/2 width=1/ qed.
+lemma cpc_cpcs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/2 width=1 by inj/ qed.
 
-lemma cpcs_strap1: ∀L,T1,T,T2. L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → L ⊢ T1 ⬌* T2.
-#L @step qed.
+lemma cpcs_strap1: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+normalize /2 width=3 by step/
+qed-.
 
-lemma cpcs_strap2: ∀L,T1,T,T2. L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
-#L @TC_strap qed.
+lemma cpcs_strap2: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+normalize /2 width=3 by TC_strap/
+qed-.
 
 (* Basic_1: was: pc3_pr2_r *)
-lemma cpr_cpcs_dx: ∀L,T1,T2. L ⊢ T1 ➡ T2 → L ⊢ T1 ⬌* T2.
-/3 width=1/ qed.
+lemma cpr_cpcs_dx: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=1 by cpc_cpcs, or_introl/ qed.
 
 (* Basic_1: was: pc3_pr2_x *)
-lemma cpr_cpcs_sn: ∀L,T1,T2. L ⊢ T2 ➡ T1 → L ⊢ T1 ⬌* T2.
-/3 width=1/ qed.
+lemma cpr_cpcs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡ T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=1 by cpc_cpcs, or_intror/ qed.
 
-lemma cpcs_cpr_strap1: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T ➡ T2 → L ⊢ T1 ⬌* T2.
-/3 width=3/ qed.
+lemma cpcs_cpr_strap1: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=3 by cpcs_strap1, or_introl/ qed-.
 
 (* Basic_1: was: pc3_pr2_u *)
-lemma cpcs_cpr_strap2: ∀L,T1,T. L ⊢ T1 ➡ T → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
-/3 width=3/ qed.
+lemma cpcs_cpr_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=3 by cpcs_strap2, or_introl/ qed-.
 
-lemma cpcs_cpr_div: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T2 ➡ T → L ⊢ T1 ⬌* T2.
-/3 width=3/ qed.
+lemma cpcs_cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=3 by cpcs_strap1, or_intror/ qed-.
 
-lemma cpr_div: ∀L,T1,T. L ⊢ T1 ➡ T → ∀T2. L ⊢ T2 ➡ T → L ⊢ T1 ⬌* T2.
-/3 width=3/ qed-.
+lemma cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=3 by cpr_cpcs_dx, cpcs_strap1, or_intror/ qed-.
 
 (* Basic_1: was: pc3_pr2_u2 *)
-lemma cpcs_cpr_conf: ∀L,T1,T. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
-/3 width=3/ qed.
+lemma cpcs_cpr_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+/3 width=3 by cpcs_strap2, or_intror/ qed-.
 
 (* Basic_1: removed theorems 9:
             clear_pc3_trans pc3_ind_left
             pc3_head_1 pc3_head_2 pc3_head_12 pc3_head_21
-            pc3_pr2_fsubst0 pc3_pr2_fsubst0_back pc3_fsubst0
+            pc3_pr2_fqubst0 pc3_pr2_fqubst0_back pc3_fqubst0
             pc3_gen_abst pc3_gen_abst_shift
 *)
 (* Basic_1: removed local theorems 6: