- commit of the "s_computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lcosx_cpx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx_cpx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx_cpx.ma
index 12b9a05d23c85502036d52d4fa32ed97ecf1d50e..756b8a7a1a740828bff1aaf329f6c28a77f16b39 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx_cpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx_cpx.ma
@@ -12,7 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/ynat/ynat_max.ma".
 include "basic_2/computation/lsx_drop.ma".
 include "basic_2/computation/lsx_lpx.ma".
 include "basic_2/computation/lsx_lpxs.ma".
@@ -22,13 +21,13 @@ include "basic_2/computation/lcosx.ma".
 
 (* Properties on extended context-sensitive parallel reduction for term *****)
 
-lemma lsx_cpx_trans_lcosx: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
-                           ∀l. G ⊢ ~⬊*[h, g, l] L →
-                           G ⊢ ⬊*[h, g, T1, l] L → G ⊢ ⬊*[h, g, T2, l] L.
-#h #g #G #L #T1 #T2 #H elim H -G -L -T1 -T2 //
+lemma lsx_cpx_trans_lcosx: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 →
+                           ∀l. G ⊢ ~⬊*[h, o, l] L →
+                           G ⊢ ⬊*[h, o, T1, l] L → G ⊢ ⬊*[h, o, T2, l] L.
+#h #o #G #L #T1 #T2 #H elim H -G -L -T1 -T2 //
 [ #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #l #HL #H
   elim (ylt_split i l) #Hli [ -H | -HL ]
-  [ <(ymax_pre_sn l (⫯i)) /2 width=1 by ylt_fwd_le_succ/
+  [ <(ymax_pre_sn l (⫯i)) /2 width=1 by ylt_fwd_le_succ1/
     elim (lcosx_drop_trans_lt … HL … HLK) // -HL -Hli
     lapply (drop_fwd_drop2 … HLK) -HLK /3 width=7 by lsx_lift_ge/
   | lapply (lsx_fwd_lref_be … H … HLK) // -H -Hli
@@ -42,8 +41,9 @@ lemma lsx_cpx_trans_lcosx: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
 | #I #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #l #HL #H
   elim (lsx_inv_flat … H) -H /3 width=1 by lsx_flat/
 | #G #L #V #U1 #U2 #T2 #_ #HTU2 #IHU12 #l #HL #H
-  elim (lsx_inv_bind … H) -H
-  /4 width=9 by lcosx_pair, lsx_inv_lift_ge, drop_drop/
+  elim (lsx_inv_bind … H) -H #HV #HU1
+  <(ypred_succ l) <yminus_SO2
+  /4 width=7 by lcosx_pair, lsx_inv_lift_ge, drop_drop/
 | #G #L #V #T1 #T2 #_ #IHT12 #l #HL #H
   elim (lsx_inv_flat … H) -H /2 width=1 by/
 | #G #L #V1 #V2 #T #_ #IHV12 #l #HL #H
@@ -57,11 +57,11 @@ lemma lsx_cpx_trans_lcosx: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
   elim (lsx_inv_flat … H) -H #HV1 #H
   elim (lsx_inv_bind … H) -H #HW1 #HT1
   @lsx_bind /2 width=1 by/ (**) (* explicit constructor *)
-  @lsx_flat [ /3 width=7 by lsx_lift_ge, drop_drop/ ]
+  @lsx_flat [ <yplus_SO2 /3 width=7 by lsx_lift_ge, drop_drop/ ]
   @(lsx_lreq_conf … (L.ⓓW1)) /3 width=1 by lcosx_pair, lreq_succ/
 ]
 qed-.
 
-lemma lsx_cpx_trans_O: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
-                       G ⊢ ⬊*[h, g, T1, 0] L → G ⊢ ⬊*[h, g, T2, 0] L.
+lemma lsx_cpx_trans_O: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, o] T2 →
+                       G ⊢ ⬊*[h, o, T1, 0] L → G ⊢ ⬊*[h, o, T2, 0] L.
 /2 width=3 by lsx_cpx_trans_lcosx/ qed-.