- improved definition of lsx allows more invariants

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpx_cpys.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cpys.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cpys.ma
index 6cb5a00ba9572ce0969b5ad993e9104ab2026896..fa1d4e8d242a0a912440029f38a2b36450efa6fd 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cpys.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_cpys.ma
@@ -17,6 +17,20 @@ include "basic_2/reduction/cpx.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
 
+(* Properties on local environment refinement for extended substitution *****)
+
+lemma lsuby_cpx_trans: ∀h,g,G. lsub_trans … (cpx h g G) (lsuby 0 (∞)).
+#h #g #G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
+[ //
+| /2 width=2 by cpx_sort/
+| #I #G #L1 #K1 #V1 #V2 #W2 #i #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
+  elim (lsuby_fwd_ldrop2_be … HL12 … HLK1) // -HL12 -HLK1 /3 width=7 by cpx_delta/
+|4,9: /4 width=1 by cpx_bind, cpx_beta, lsuby_pair_O_Y/
+|5,7,8: /3 width=1 by cpx_flat, cpx_tau, cpx_ti/
+|6,10: /4 width=3 by cpx_zeta, cpx_theta, lsuby_pair_O_Y/
+]
+qed-.
+
 (* Properties on context-sensitive extended multiple substitution for terms *)
 
 lemma cpys_cpx: ∀h,g,G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*[d, e] T2 → ⦃G, L⦄ ⊢ T1 ➡[h, g] T2.