milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / computation / lcosx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/computation/lcosx.ma b/matita/matita/contribs/lambdadelta/basic_2A/computation/lcosx.ma
index c779101348aac79a8cc5fd8954b9e297aae629e8..465a42cd0316f4a1ae5824833262f9f5546bd0a7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2A/computation/lcosx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2A/computation/lcosx.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/ynat/ynat_minus_sn.ma".
 include "basic_2A/notation/relations/cosn_5.ma".
 include "basic_2A/computation/lsx.ma".
 
@@ -21,7 +22,7 @@ inductive lcosx (h) (g) (G): relation2 ynat lenv ≝
 | lcosx_sort: ∀l. lcosx h g G l (⋆)
 | lcosx_skip: ∀I,L,T. lcosx h g G 0 L → lcosx h g G 0 (L.ⓑ{I}T)
 | lcosx_pair: ∀I,L,T,l. G ⊢ ⬊*[h, g, T, l] L →
-              lcosx h g G l L â\86\92 lcosx h g G (⫯l) (L.ⓑ{I}T)
+              lcosx h g G l L â\86\92 lcosx h g G (â\86\91l) (L.ⓑ{I}T)
 .
 
 interpretation
@@ -36,7 +37,7 @@ qed.
 
 lemma lcosx_drop_trans_lt: ∀h,g,G,L,l. G ⊢ ~⬊*[h, g, l] L →
                             ∀I,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → i < l →
-                            G â\8a¢ ~â¬\8a*[h, g, â«°(l-i)] K â\88§ G â\8a¢ â¬\8a*[h, g, V, â«°(l-i)] K.
+                            G â\8a¢ ~â¬\8a*[h, g, â\86\93(l-i)] K â\88§ G â\8a¢ â¬\8a*[h, g, V, â\86\93(l-i)] K.
 #h #g #G #L #l #H elim H -L -l
 [ #l #J #K #V #i #H elim (drop_inv_atom1 … H) -H #H destruct
 | #I #L #T #_ #_ #J #K #V #i #_ #H elim (ylt_yle_false … H) -H //
@@ -44,7 +45,7 @@ lemma lcosx_drop_trans_lt: ∀h,g,G,L,l. G ⊢ ~⬊*[h, g, l] L →
   elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK destruct
   [ >ypred_succ /2 width=1 by conj/
   | lapply (ylt_pred … Hil ?) -Hil /2 width=1 by ylt_inj/ >ypred_succ #Hil
-    elim (IHL … HLK ?) -IHL -HLK <yminus_inj >yminus_SO2 //
+    elim (IHL … HLK ?) -IHL -HLK >minus_SO_dx //
     <(ypred_succ l) in ⊢ (%→%→?); >yminus_pred /2 width=1 by ylt_inj, conj/
   ]
 ]
@@ -52,23 +53,23 @@ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lcosx_inv_succ_aux: â\88\80h,g,G,L,x. G â\8a¢ ~â¬\8a*[h, g, x] L â\86\92 â\88\80l. x = ⫯l →
+fact lcosx_inv_succ_aux: â\88\80h,g,G,L,x. G â\8a¢ ~â¬\8a*[h, g, x] L â\86\92 â\88\80l. x = â\86\91l →
                          L = ⋆ ∨
                          ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, l] K &
                                   G ⊢ ⬊*[h, g, V, l] K.
 #h #g #G #L #l * -L -l /2 width=1 by or_introl/
 [ #I #L #T #_ #x #H elim (ysucc_inv_O_sn … H)
-| #I #L #T #l #HT #HL #x #H <(ysucc_inj … H) -x
+| #I #L #T #l #HT #HL #x #H <(ysucc_inv_inj … H) -x
   /3 width=6 by ex3_3_intro, or_intror/
 ]
 qed-.
 
-lemma lcosx_inv_succ: â\88\80h,g,G,L,l. G â\8a¢ ~â¬\8a*[h, g, ⫯l] L → L = ⋆ ∨
+lemma lcosx_inv_succ: â\88\80h,g,G,L,l. G â\8a¢ ~â¬\8a*[h, g, â\86\91l] L → L = ⋆ ∨
                       ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, l] K &
                                G ⊢ ⬊*[h, g, V, l] K.
 /2 width=3 by lcosx_inv_succ_aux/ qed-.
 
-lemma lcosx_inv_pair: â\88\80h,g,I,G,L,T,l. G â\8a¢ ~â¬\8a*[h, g, ⫯l] L.ⓑ{I}T →
+lemma lcosx_inv_pair: â\88\80h,g,I,G,L,T,l. G â\8a¢ ~â¬\8a*[h, g, â\86\91l] L.ⓑ{I}T →
                       G ⊢ ~⬊*[h, g, l] L ∧ G ⊢ ⬊*[h, g, T, l] L.
 #h #g #I #G #L #T #l #H elim (lcosx_inv_succ … H) -H
 [ #H destruct