- revision of ground_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma
index 102ed0cebef192a09580e9836d9e5d0ec4af0009..2c693baaa79f566c131d6991c96b02ce42b007e3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/ynat/ynat_max.ma".
 include "basic_2/substitution/lift_lift.ma".
 include "basic_2/multiple/mr2_minus.ma".
 include "basic_2/multiple/lifts.ma".
@@ -37,7 +38,7 @@ lemma lifts_lift_trans: ∀cs,i,i0. @⦃i, cs⦄ ≡ i0 →
                         ∀T1,T0. ⬆*[cs0] T1 ≡ T0 →
                         ∀T2. ⬆[O, i0 + 1] T0 ≡ T2 →
                         ∃∃T. ⬆[0, i + 1] T1 ≡ T & ⬆*[cs] T ≡ T2.
-#cs elim cs -cs normalize
+#cs elim cs -cs
 [ #i #x #H1 #cs0 #H2 #T1 #T0 #HT10 #T2
   <(at_inv_nil … H1) -x #HT02
   lapply (minuss_inv_nil1 … H2) -H2 #H
@@ -45,15 +46,18 @@ lemma lifts_lift_trans: ∀cs,i,i0. @⦃i, cs⦄ ≡ i0 →
   >(lifts_inv_nil … H) -T1 /2 width=3 by lifts_nil, ex2_intro/
 | #l #m #cs #IHcs #i #i0 #H1 #cs0 #H2 #T1 #T0 #HT10 #T2 #HT02
   elim (at_inv_cons … H1) -H1 * #Hil #Hi0
-  [ elim (minuss_inv_cons1_lt … H2) -H2 [2: /2 width=1 by lt_minus_to_plus/ ] #cs1 #Hcs1 <minus_le_minus_minus_comm // <minus_plus_m_m #H
+  [ elim (minuss_inv_cons1_lt … H2) -H2 /2 width=1 by ylt_succ/ #cs1 #Hcs1
+    <yplus_inj >yplus_SO2 >yplus_SO2 >yminus_succ #H
     elim (pluss_inv_cons2 … H) -H #cs2 #H1 #H2 destruct
-    elim (lifts_inv_cons … HT10) -HT10 #T >minus_plus #HT1 #HT0
+    elim (lifts_inv_cons … HT10) -HT10 #T #HT1 #HT0
     elim (IHcs … Hi0 … Hcs1 … HT0 … HT02) -IHcs -Hi0 -Hcs1 -T0 #T0 #HT0 #HT02
-    elim (lift_trans_le … HT1 … HT0) -T /2 width=1 by/ #T #HT1 <plus_minus_m_m /3 width=5 by lifts_cons, ex2_intro/
+    elim (lift_trans_le … HT1 … HT0) -T /2 width=1 by/ #T #HT1
+    <yminus_plus2 <yplus_inj >yplus_SO2 >ymax_pre_sn
+    /3 width=5 by lifts_cons, ex2_intro, ylt_fwd_le_succ1/
   | >commutative_plus in Hi0; #Hi0
-    lapply (minuss_inv_cons1_ge … H2 ?) -H2 [ /2 width=1 by le_S_S/ ] <associative_plus #Hcs0
+    lapply (minuss_inv_cons1_ge … H2 ?) -H2 /2 width=1 by yle_succ/ <associative_plus #Hcs0
     elim (IHcs … Hi0 … Hcs0 … HT10 … HT02) -IHcs -Hi0 -Hcs0 -T0 #T0 #HT0 #HT02
-    elim (lift_split … HT0 l (i+1)) -HT0 /3 width=5 by lifts_cons, le_S, ex2_intro/
+    elim (lift_split … HT0 l (i+1)) -HT0 /3 width=5 by lifts_cons, yle_succ, yle_pred_sn, ex2_intro/
   ]
 ]
 qed-.