- ldrop is now drop as in basic_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / llpx_sn_leq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_leq.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_leq.ma
index 8334d161416af1b1ebf37028bba1fdd6059104bc..5075a332e1233ba255c0bb6d473df369e87bde98 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_leq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_leq.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/ldrop_leq.ma".
+include "basic_2/substitution/drop_leq.ma".
 include "basic_2/multiple/llpx_sn.ma".
 
 (* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
@@ -20,11 +20,11 @@ include "basic_2/multiple/llpx_sn.ma".
 (* Properties on equivalence for local environments *************************)
 
 lemma leq_llpx_sn_trans: ∀R,L2,L,T,d. llpx_sn R d T L2 L →
-                         â\88\80L1. L1 â\89\83[d, ∞] L2 → llpx_sn R d T L1 L.
+                         â\88\80L1. L1 ⩬[d, ∞] L2 → llpx_sn R d T L1 L.
 #R #L2 #L #T #d #H elim H -L2 -L -T -d
 /4 width=5 by llpx_sn_flat, llpx_sn_gref, llpx_sn_skip, llpx_sn_sort, leq_fwd_length, trans_eq/  
 [ #I #L2 #L #K2 #K #V2 #V #d #i #Hdi #HLK2 #HLK #HK2 #HV2 #_ #L1 #HL12
-  elim (leq_ldrop_trans_be … HL12 … HLK2) -L2 // >yminus_Y_inj #K1 #HK12 #HLK1
+  elim (leq_drop_trans_be … HL12 … HLK2) -L2 // >yminus_Y_inj #K1 #HK12 #HLK1
   lapply (leq_inv_O_Y … HK12) -HK12 #H destruct /2 width=9 by llpx_sn_lref/
 | /4 width=5 by llpx_sn_free, leq_fwd_length, le_repl_sn_trans_aux, trans_eq/
 | /4 width=1 by llpx_sn_bind, leq_succ/
@@ -32,19 +32,19 @@ lemma leq_llpx_sn_trans: ∀R,L2,L,T,d. llpx_sn R d T L2 L →
 qed-.
 
 lemma llpx_sn_leq_trans: ∀R,L,L1,T,d. llpx_sn R d T L L1 →
-                         â\88\80L2. L1 â\89\83[d, ∞] L2 → llpx_sn R d T L L2.
+                         â\88\80L2. L1 ⩬[d, ∞] L2 → llpx_sn R d T L L2.
 #R #L #L1 #T #d #H elim H -L -L1 -T -d
 /4 width=5 by llpx_sn_flat, llpx_sn_gref, llpx_sn_skip, llpx_sn_sort, leq_fwd_length, trans_eq/  
 [ #I #L #L1 #K #K1 #V #V1 #d #i #Hdi #HLK #HLK1 #HK1 #HV1 #_ #L2 #HL12
-  elim (leq_ldrop_conf_be … HL12 … HLK1) -L1 // >yminus_Y_inj #K2 #HK12 #HLK2
+  elim (leq_drop_conf_be … HL12 … HLK1) -L1 // >yminus_Y_inj #K2 #HK12 #HLK2
   lapply (leq_inv_O_Y … HK12) -HK12 #H destruct /2 width=9 by llpx_sn_lref/
 | /4 width=5 by llpx_sn_free, leq_fwd_length, le_repl_sn_conf_aux, trans_eq/
 | /4 width=1 by llpx_sn_bind, leq_succ/
 ]
 qed-.
 
-lemma llpx_sn_leq_repl: â\88\80R,L1,L2,T,d. llpx_sn R d T L1 L2 â\86\92 â\88\80K1. K1 â\89\83[d, ∞] L1 → 
-                        â\88\80K2. L2 â\89\83[d, ∞] K2 → llpx_sn R d T K1 K2.
+lemma llpx_sn_leq_repl: â\88\80R,L1,L2,T,d. llpx_sn R d T L1 L2 â\86\92 â\88\80K1. K1 ⩬[d, ∞] L1 → 
+                        â\88\80K2. L2 ⩬[d, ∞] K2 → llpx_sn R d T K1 K2.
 /3 width=4 by llpx_sn_leq_trans, leq_llpx_sn_trans/ qed-.
 
 lemma llpx_sn_bind_repl_SO: ∀R,I1,I2,L1,L2,V1,V2,T. llpx_sn R 0 T (L1.ⓑ{I1}V1) (L2.ⓑ{I2}V2) →