universary milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_llpx_sn.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_llpx_sn.ma
index 41810649416a878f3ed38bb903f0a2fef4f5aea3..001b3c0e1b6b72a1b012411a3c77a89b03fd25e6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_llpx_sn.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_llpx_sn.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/llpx_sn_ldrop.ma".
+include "basic_2/multiple/llpx_sn_drop.ma".
 include "basic_2/reduction/cpx.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
@@ -20,24 +20,22 @@ include "basic_2/reduction/cpx.ma".
 (* Properties on lazy sn pointwise extensions *******************************)
 
 (* Note: lemma 1000 *)
-lemma cpx_llpx_sn_conf: ∀R. (∀I,L.reflexive … (R I L)) →
-                            (∀I.l_liftable (R I)) →
-                            (∀I.l_deliftable_sn (R I)) →
-                        ∀h,g,G. s_r_confluent1 … (cpx h g G) (llpx_sn R 0).
-#R #H1R #H2R #H3R #h #g #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
+lemma cpx_llpx_sn_conf: ∀R. (∀L. reflexive … (R L)) → d_liftable R → d_deliftable_sn R →
+                        ∀h,o,G. c_r_confluent1 … (cpx h o G) (llpx_sn R 0).
+#R #H1R #H2R #H3R #h #o #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
 [ //
 | /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/
-| #I #G #Ls #Ks #V1s #V2s #W2s #i #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
-  #Kd #V1d #HLKd #HV1s #HV1sd
-  lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
-  lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
-  @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
+| #I #G #Ls #Ks #V1c #V2c #W2c #i #HLKs #_ #HVW2c #IHV12c #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
+  #Kd #V1l #HLKd #HV1c #HV1sd
+  lapply (drop_fwd_drop2 … HLKs) -HLKs #HLKs
+  lapply (drop_fwd_drop2 … HLKd) -HLKd #HLKd
+  @(llpx_sn_lift_le … HLKs HLKd … HVW2c) -HLKs -HLKd -HVW2c /2 width=1 by/ (**) (* full auto too slow *)
 | #a #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_bind/
 | #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
   /3 width=1 by llpx_sn_flat/
 | #G #Ls #V #T1 #T2 #T #_ #HT2 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
-  /3 width=10 by llpx_sn_inv_lift_le, ldrop_drop/
+  /3 width=10 by llpx_sn_inv_lift_le, drop_drop/
 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H /2 width=1 by/
 | #G #Ls #V1 #V2 #T #_ #IHV12 #Ld #H elim (llpx_sn_inv_flat … H) -H /2 width=1 by/
 | #a #G #Ls #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
@@ -46,7 +44,7 @@ lemma cpx_llpx_sn_conf: ∀R. (∀I,L.reflexive … (R I L)) →
 | #a #G #Ls #V1 #V2 #V #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
   #HV1 #H elim (llpx_sn_inv_bind_O … H) -H //
   #HW1 #HT1 @llpx_sn_bind_O /2 width=1 by/ @llpx_sn_flat (**) (* full auto too slow *)
-  [ /3 width=10 by llpx_sn_lift_le, ldrop_drop/
+  [ /3 width=10 by llpx_sn_lift_le, drop_drop/
   | /3 width=4 by llpx_sn_bind_repl_O/
 ]
 qed-.