update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
index e8ecc622c339fa50d052936b709803806e9be15f..75964c6159eaec418568c095317df546891f1b28 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
@@ -18,7 +18,7 @@ include "basic_2/conversion/cpc.ma".
 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
 
 definition cpcs: relation4 genv lenv term term ≝
-           λG. LTC … (cpc G).
+           λG. CTC … (cpc G).
 
 interpretation "context-sensitive parallel equivalence (term)"
    'PConvStar G L T1 T2 = (cpcs G L T1 T2).
@@ -28,59 +28,61 @@ interpretation "context-sensitive parallel equivalence (term)"
 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.
-#G #L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
+normalize /3 width=6 by TC_star_ind/
 qed-.
 
 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.
-#G #L #T2 #R #HT2 #IHT2 #T1 #HT12
-@(TC_star_ind_dx … HT2 IHT2 … HT12) //
+normalize /3 width=6 by TC_star_ind_dx/
 qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: pc3_refl *)
 lemma cpcs_refl: ∀G,L. reflexive … (cpcs G L).
-/2 width=1/ qed.
+/2 width=1 by inj/ qed.
 
 (* Basic_1: was: pc3_s *)
 lemma cpcs_sym: ∀G,L. symmetric … (cpcs G L).
-#G #L @TC_symmetric // qed.
+normalize /3 width=1 by cpc_sym, TC_symmetric/
+qed-.
 
-lemma cpc_cpcs: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ⦃G, 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: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌* T → ⦃G, L⦄ ⊢ T ⬌ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L @step qed.
+normalize /2 width=3 by step/
+qed-.
 
 lemma cpcs_strap2: ∀G,L,T1,T,T2. ⦃G, L⦄ ⊢ T1 ⬌ T → ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L @TC_strap qed.
+normalize /2 width=3 by TC_strap/
+qed-.
 
 (* Basic_1: was: pc3_pr2_r *)
 lemma cpr_cpcs_dx: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-/3 width=1/ qed.
+/3 width=1 by cpc_cpcs, or_introl/ qed.
 
 (* Basic_1: was: pc3_pr2_x *)
 lemma cpr_cpcs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡ T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-/3 width=1/ qed.
+/3 width=1 by cpc_cpcs, or_intror/ 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/ qed.
+/3 width=3 by cpcs_strap1, or_introl/ qed-.
 
 (* Basic_1: was: pc3_pr2_u *)
 lemma cpcs_cpr_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-/3 width=3/ qed.
+/3 width=3 by cpcs_strap2, or_introl/ 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/ qed.
+/3 width=3 by cpcs_strap1, or_intror/ qed-.
 
 lemma cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-/3 width=3/ qed-.
+/3 width=3 by cpr_cpcs_dx, cpcs_strap1, or_intror/ qed-.
 
 (* Basic_1: was: pc3_pr2_u2 *)
 lemma cpcs_cpr_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-/3 width=3/ qed.
+/3 width=3 by cpcs_strap2, or_intror/ qed-.
 
 (* Basic_1: removed theorems 9:
             clear_pc3_trans pc3_ind_left