update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_cpcs.ma
index aa22846fde6705d82383c6d92bb5b5bf1fa70458..f8ef46db1a196853a2f7f029d90fa92782d68302 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/scpes_cpcs.ma
@@ -20,20 +20,20 @@ include "basic_2/equivalence/scpes.ma".
 
 (* Inversion lemmas on parallel equivalence for terms ***********************)
 
-lemma scpes_inv_lstas_eq: ∀h,g,G,L,T1,T2,l1,l2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2 →
-                          ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, l1] U1 →
-                          ∀U2. ⦃G, L⦄ ⊢ T2 •*[h, l2] U2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
-#h #g #G #L #T1 #T2 #l1 #l2 * #T #HT1 #HT2 #U1 #HTU1 #U2 #HTU2
+lemma scpes_inv_lstas_eq: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
+                          ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, d1] U1 →
+                          ∀U2. ⦃G, L⦄ ⊢ T2 •*[h, d2] U2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
+#h #o #G #L #T1 #T2 #d1 #d2 * #T #HT1 #HT2 #U1 #HTU1 #U2 #HTU2
 /3 width=8 by scpds_inv_lstas_eq, cprs_div/
 qed-.
 
 (* Properties on parallel equivalence for terms *****************************)
 
-lemma cpcs_scpes: ∀h,g,G,L,T1,l11. ⦃G, L⦄ ⊢ T1 ▪[h, g] l11 →
-                  ∀U1,l12. l12 ≤ l11 → ⦃G, L⦄ ⊢ T1 •*[h, l12] U1 →
-                  ∀T2,l21. ⦃G, L⦄ ⊢ T2 ▪[h, g] l21 →
-                  ∀U2,l22. l22 ≤ l21 → ⦃G, L⦄ ⊢ T2 •*[h, l22] U2 →
-                  ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, l12, l22] T2.
-#h #g #G #L #T1 #l11 #HT1 #U1 #l12 #Hl121 #HTU1 #T2 #l21 #HT2 #U2 #l22 #Hl221 #HTU2 #HU12
+lemma cpcs_scpes: ∀h,o,G,L,T1,d11. ⦃G, L⦄ ⊢ T1 ▪[h, o] d11 →
+                  ∀U1,d12. d12 ≤ d11 → ⦃G, L⦄ ⊢ T1 •*[h, d12] U1 →
+                  ∀T2,d21. ⦃G, L⦄ ⊢ T2 ▪[h, o] d21 →
+                  ∀U2,d22. d22 ≤ d21 → ⦃G, L⦄ ⊢ T2 •*[h, d22] U2 →
+                  ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d12, d22] T2.
+#h #o #G #L #T1 #d11 #HT1 #U1 #d12 #Hd121 #HTU1 #T2 #d21 #HT2 #U2 #d22 #Hd221 #HTU2 #HU12
 elim (cpcs_inv_cprs … HU12) -HU12 /3 width=6 by scpds_div, ex4_2_intro/
 qed.