- some renaming according to the written version of 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 efa5038d27e580b5510ca78586bbe9ae4e8ad225..990878bee5b0200938f21e6321a908b4156c241f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/substitution/lift_lift.ma".
-include "basic_2/multiple/gr2_minus.ma".
+include "basic_2/multiple/mr2_minus.ma".
 include "basic_2/multiple/lifts.ma".
 
 (* GENERIC TERM RELOCATION **************************************************)
@@ -21,11 +21,11 @@ include "basic_2/multiple/lifts.ma".
 (* Properties concerning basic term relocation ******************************)
 
 (* Basic_1: was: lift1_xhg (right to left) *)
-lemma lifts_lift_trans_le: â\88\80T1,T,des. â\87§*[des] T1 â\89¡ T â\86\92 â\88\80T2. â\87§[0, 1] T ≡ T2 →
-                           â\88\83â\88\83T0. â\87§[0, 1] T1 â\89¡ T0 & â\87§*[des + 1] T0 ≡ T2.
+lemma lifts_lift_trans_le: â\88\80T1,T,des. â¬\86*[des] T1 â\89¡ T â\86\92 â\88\80T2. â¬\86[0, 1] T ≡ T2 →
+                           â\88\83â\88\83T0. â¬\86[0, 1] T1 â\89¡ T0 & â¬\86*[des + 1] T0 ≡ T2.
 #T1 #T #des #H elim H -T1 -T -des
 [ /2 width=3/
-| #T1 #T3 #T #des #d #e #HT13 #_ #IHT13 #T2 #HT2
+| #T1 #T3 #T #des #l #m #HT13 #_ #IHT13 #T2 #HT2
   elim (IHT13 … HT2) -T #T #HT3 #HT2
   elim (lift_trans_le … HT13 … HT3) -T3 // /3 width=5/
 ]
@@ -34,26 +34,26 @@ qed-.
 (* Basic_1: was: lift1_free (right to left) *)
 lemma lifts_lift_trans: ∀des,i,i0. @⦃i, des⦄ ≡ i0 →
                         ∀des0. des + 1 ▭ i + 1 ≡ des0 + 1 →
-                        â\88\80T1,T0. â\87§*[des0] T1 ≡ T0 →
-                        â\88\80T2. â\87§[O, i0 + 1] T0 ≡ T2 →
-                        â\88\83â\88\83T. â\87§[0, i + 1] T1 â\89¡ T & â\87§*[des] T ≡ T2.
+                        â\88\80T1,T0. â¬\86*[des0] T1 ≡ T0 →
+                        â\88\80T2. â¬\86[O, i0 + 1] T0 ≡ T2 →
+                        â\88\83â\88\83T. â¬\86[0, i + 1] T1 â\89¡ T & â¬\86*[des] T ≡ T2.
 #des elim des -des normalize
 [ #i #x #H1 #des0 #H2 #T1 #T0 #HT10 #T2
   <(at_inv_nil … H1) -x #HT02
   lapply (minuss_inv_nil1 … H2) -H2 #H
   >(pluss_inv_nil2 … H) in HT10; -des0 #H
   >(lifts_inv_nil … H) -T1 /2 width=3/
-| #d #e #des #IHdes #i #i0 #H1 #des0 #H2 #T1 #T0 #HT10 #T2 #HT02
-  elim (at_inv_cons … H1) -H1 * #Hid #Hi0
-  [ elim (minuss_inv_cons1_lt … H2) -H2 [2: /2 width=1/ ] #des1 #Hdes1 <minus_le_minus_minus_comm // <minus_plus_m_m #H
+| #l #m #des #IHcs #i #i0 #H1 #des0 #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/ ] #des1 #Hcs1 <minus_le_minus_minus_comm // <minus_plus_m_m #H
     elim (pluss_inv_cons2 … H) -H #des2 #H1 #H2 destruct
     elim (lifts_inv_cons … HT10) -HT10 #T >minus_plus #HT1 #HT0
-    elim (IHdes … Hi0 … Hdes1 … HT0 … HT02) -IHdes -Hi0 -Hdes1 -T0 #T0 #HT0 #HT02
+    elim (IHcs … Hi0 … Hcs1 … HT0 … HT02) -IHcs -Hi0 -Hcs1 -T0 #T0 #HT0 #HT02
     elim (lift_trans_le … HT1 … HT0) -T /2 width=1/ #T #HT1 <plus_minus_m_m /2 width=1/ /3 width=5/
   | >commutative_plus in Hi0; #Hi0
-    lapply (minuss_inv_cons1_ge … H2 ?) -H2 [ /2 width=1/ ] <associative_plus #Hdes0
-    elim (IHdes … Hi0 … Hdes0 … HT10 … HT02) -IHdes -Hi0 -Hdes0 -T0 #T0 #HT0 #HT02
-    elim (lift_split … HT0 d (i+1)) -HT0 /2 width=1/ /3 width=5/
+    lapply (minuss_inv_cons1_ge … H2 ?) -H2 [ /2 width=1/ ] <associative_plus #Hcs0
+    elim (IHcs … Hi0 … Hcs0 … HT10 … HT02) -IHcs -Hi0 -Hcs0 -T0 #T0 #HT0 #HT02
+    elim (lift_split … HT0 l (i+1)) -HT0 /2 width=1/ /3 width=5/
   ]
 ]
 qed-.