- a reinforement in a lemma on ldrop allows to prove a lemma on lsx :)

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/crx_append.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/crx_append.ma
index bd91ad1d5c1f2ebd5250605ee9b91e7ed07d6759..56667b20f28db966fb14943f3b5b87c82f2eafcf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/crx_append.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/crx_append.ma
@@ -15,17 +15,18 @@
 include "basic_2/relocation/ldrop_append.ma".
 include "basic_2/reduction/crx.ma".
 
-(* CONTEXT-SENSITIVE EXTENDED REDUCIBLE TERMS *******************************)
+(* REDUCIBLE TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION *****************)
 
 (* Advanved properties ******************************************************)
 
-lemma crx_append_sn: ∀h,g,L,K,T. ⦃G, L⦄ ⊢ 𝐑[h, g]⦃T⦄  → ⦃h, K @@ L⦄ ⊢ 𝐑[h, g]⦃T⦄.
-#h #g #L #K0 #T #H elim H -L -T /2 width=1/ /2 width=2/
+lemma crx_append_sn: ∀h,g,G,L,K,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄  → ⦃G, K @@ L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄.
+#h #g #G #L #K0 #T #H elim H -L -T
+/2 width=2 by crx_sort, crx_appl_sn, crx_appl_dx, crx_ri2, crx_ib2_sn, crx_ib2_dx, crx_beta, crx_theta/
 #I #L #K #V #i #HLK
 lapply (ldrop_fwd_length_lt2 … HLK) #Hi
-lapply (ldrop_O1_append_sn_le … HLK … K0) -HLK /2 width=2/ -Hi /2 width=4/
+lapply (ldrop_O1_append_sn_le … HLK … K0) -HLK /2 width=4 by crx_delta, lt_to_le/
 qed.
 
-lemma trx_crx: ∀h,g,L,T. ⦃h, ⋆⦄ ⊢ 𝐑[h, g]⦃T⦄ → ⦃G, L⦄ ⊢ 𝐑[h, g]⦃T⦄.
-#h #g #L #T #H lapply (crx_append_sn … H) //
+lemma trx_crx: ∀h,g,G,L,T. ⦃G, ⋆⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄.
+#h #g #G #L #T #H lapply (crx_append_sn … H) //
 qed.