milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / cpss.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/cpss.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/cpss.ma
index 993669ad4d1046c88cd5a53ffb1d661002596043..9789ea7bad615f0d1a49e8c51eb43e8ef7567a2f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/cpss.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/cpss.ma
@@ -12,7 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/grammar/cl_shift.ma".
 include "basic_2/relocation/ldrop_append.ma".
+include "basic_2/substitution/lsubr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL SUBSTITUTION FOR TERMS ************************)
 
@@ -34,16 +36,11 @@ interpretation "context-sensitive parallel substitution (term)"
 
 (* Basic properties *********************************************************)
 
-(* Note: it does not hold replacing |L1| with |L2| *)
-lemma cpss_lsubr_trans: ∀L1,T1,T2. L1 ⊢ T1 ▶* T2 →
-                        ∀L2. L2 ⊑ [0, |L1|] L1 → L2 ⊢ T1 ▶* T2.
+lemma cpss_lsubr_trans: lsub_trans … cpss lsubr.
 #L1 #T1 #T2 #H elim H -L1 -T1 -T2
 [ //
 | #L1 #K1 #V1 #V2 #W2 #i #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
-  lapply (ldrop_fwd_ldrop2_length … HLK1) #Hi
-  lapply (ldrop_fwd_O1_length … HLK1) #H2i
-  elim (ldrop_lsubr_ldrop2_abbr … HL12 … HLK1 ? ?) -HL12 -HLK1 // -Hi
-  <H2i -H2i <minus_plus_m_m /3 width=6/
+  elim (lsubr_fwd_ldrop2_abbr … HL12 … HLK1) -HL12 -HLK1 /3 width=6/
 | /4 width=1/
 | /3 width=1/
 ]
@@ -63,10 +60,10 @@ lemma cpss_delift: ∀K,V,T1,L,d. ⇩[0, d] L ≡ (K. ⓓV) →
   elim (lt_or_eq_or_gt i d) #Hid /3 width=4/
   destruct
   elim (lift_total V 0 (i+1)) #W #HVW
-  elim (lift_split … HVW i i ? ? ?) // /3 width=6/
+  elim (lift_split … HVW i i) // /3 width=6/
 | * [ #a ] #I #W1 #U1 #IHW1 #IHU1 #L #d #HLK
   elim (IHW1 … HLK) -IHW1 #W2 #W #HW12 #HW2
-  [ elim (IHU1 (L. ⓑ{I} W1) (d+1) ?) -IHU1 /2 width=1/ -HLK /3 width=9/
+  [ elim (IHU1 (L. ⓑ{I} W1) (d+1)) -IHU1 /2 width=1/ -HLK /3 width=9/
   | elim (IHU1 … HLK) -IHU1 -HLK /3 width=8/
   ]
 ]
@@ -75,7 +72,7 @@ qed-.
 lemma cpss_append: l_appendable_sn … cpss.
 #K #T1 #T2 #H elim H -K -T1 -T2 // /2 width=1/
 #K #K0 #V1 #V2 #W2 #i #HK0 #_ #HVW2 #IHV12 #L
-lapply (ldrop_fwd_ldrop2_length … HK0) #H
+lapply (ldrop_fwd_length_lt2 … HK0) #H
 @(cpss_delta … (L@@K0) V1 … HVW2) //
 @(ldrop_O1_append_sn_le … HK0) /2 width=2/ (**) (* /3/ does not work *)
 qed.