- the trace is explicit in all auto tactics with depth > 1

[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 990878bee5b0200938f21e6321a908b4156c241f..102ed0cebef192a09580e9836d9e5d0ec4af0009 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/lifts_lift.ma
@@ -21,39 +21,39 @@ include "basic_2/multiple/lifts.ma".
 (* Properties concerning basic term relocation ******************************)
 
 (* Basic_1: was: lift1_xhg (right to left) *)
-lemma lifts_lift_trans_le: ∀T1,T,des. ⬆*[des] T1 ≡ T → ∀T2. ⬆[0, 1] T ≡ T2 →
-                           ∃∃T0. ⬆[0, 1] T1 ≡ T0 & ⬆*[des + 1] T0 ≡ T2.
-#T1 #T #des #H elim H -T1 -T -des
-[ /2 width=3/
-| #T1 #T3 #T #des #l #m #HT13 #_ #IHT13 #T2 #HT2
+lemma lifts_lift_trans_le: ∀T1,T,cs. ⬆*[cs] T1 ≡ T → ∀T2. ⬆[0, 1] T ≡ T2 →
+                           ∃∃T0. ⬆[0, 1] T1 ≡ T0 & ⬆*[cs + 1] T0 ≡ T2.
+#T1 #T #cs #H elim H -T1 -T -cs
+[ /2 width=3 by lifts_nil, ex2_intro/
+| #T1 #T3 #T #cs #l #m #HT13 #_ #IHT13 #T2 #HT2
   elim (IHT13 … HT2) -T #T #HT3 #HT2
-  elim (lift_trans_le … HT13 … HT3) -T3 // /3 width=5/
+  elim (lift_trans_le … HT13 … HT3) -T3 /3 width=5 by lifts_cons, ex2_intro/
 ]
 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 →
-                        ∀T1,T0. ⬆*[des0] T1 ≡ T0 →
+lemma lifts_lift_trans: ∀cs,i,i0. @⦃i, cs⦄ ≡ i0 →
+                        ∀cs0. cs + 1 ▭ i + 1 ≡ cs0 + 1 →
+                        ∀T1,T0. ⬆*[cs0] T1 ≡ T0 →
                         ∀T2. ⬆[O, i0 + 1] T0 ≡ T2 →
-                        ∃∃T. ⬆[0, i + 1] T1 ≡ T & ⬆*[des] T ≡ T2.
-#des elim des -des normalize
-[ #i #x #H1 #des0 #H2 #T1 #T0 #HT10 #T2
+                        ∃∃T. ⬆[0, i + 1] T1 ≡ T & ⬆*[cs] T ≡ T2.
+#cs elim cs -cs normalize
+[ #i #x #H1 #cs0 #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/
-| #l #m #des #IHcs #i #i0 #H1 #des0 #H2 #T1 #T0 #HT10 #T2 #HT02
+  >(pluss_inv_nil2 … H) in HT10; -cs0 #H
+  >(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/ ] #des1 #Hcs1 <minus_le_minus_minus_comm // <minus_plus_m_m #H
-    elim (pluss_inv_cons2 … H) -H #des2 #H1 #H2 destruct
+  [ 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 (pluss_inv_cons2 … H) -H #cs2 #H1 #H2 destruct
     elim (lifts_inv_cons … HT10) -HT10 #T >minus_plus #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/ #T #HT1 <plus_minus_m_m /2 width=1/ /3 width=5/
+    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/
   | >commutative_plus in Hi0; #Hi0
-    lapply (minuss_inv_cons1_ge … H2 ?) -H2 [ /2 width=1/ ] <associative_plus #Hcs0
+    lapply (minuss_inv_cons1_ge … H2 ?) -H2 [ /2 width=1 by le_S_S/ ] <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/
+    elim (lift_split … HT0 l (i+1)) -HT0 /3 width=5 by lifts_cons, le_S, ex2_intro/
   ]
 ]
 qed-.