- revision of ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / cpy_nlift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_nlift.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_nlift.ma
index bcf52015d7d921bdc2a930df6c1cce0eea84e915..3a645072473619d7ca7cf66389a381c5e7f13009 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_nlift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/cpy_nlift.ma
@@ -21,18 +21,18 @@ include "basic_2/substitution/cpy.ma".
 (* Inversion lemmas on negated relocation ***********************************)
 
 lemma cpy_fwd_nlift2_ge: ∀G,L,U1,U2,l,m. ⦃G, L⦄ ⊢ U1 ▶[l, m] U2 →
-                         ∀i. l ≤ yinj i → (∀T2. ⬆[i, 1] T2 ≡ U2 → ⊥) →
+                         ∀i. l ≤ i → (∀T2. ⬆[i, 1] T2 ≡ U2 → ⊥) →
                          (∀T1. ⬆[i, 1] T1 ≡ U1 → ⊥) ∨
                          ∃∃I,K,W,j. l ≤ yinj j & j < i & ⬇[j]L ≡ K.ⓑ{I}W &
-                                    (∀V. ⬆[i-j-1, 1] V ≡ W → ⊥) & (∀T1. ⬆[j, 1] T1 ≡ U1 → ⊥).
+                                    (∀V. ⬆[⫰(i-j), 1] V ≡ W → ⊥) & (∀T1. ⬆[j, 1] T1 ≡ U1 → ⊥).
 #G #L #U1 #U2 #l #m #H elim H -G -L -U1 -U2 -l -m
 [ /3 width=2 by or_introl/
 | #I #G #L #K #V #W #j #l #m #Hlj #Hjlm #HLK #HVW #i #Hli #HnW
-  elim (lt_or_ge j i) #Hij
+  elim (ylt_split j i) #Hij
   [ @or_intror @(ex5_4_intro … HLK) // -HLK
-    [ #X #HXV elim (lift_trans_le … HXV … HVW ?) -V //
-      #Y #HXY >minus_plus <plus_minus_m_m /2 width=2 by/
-    | -HnW /2 width=7 by lift_inv_lref2_be/
+    [ #X #HXV elim (lift_trans_le … HXV … HVW ?) -V // #Y #HXY
+      <yminus_succ2 <yplus_inj >yplus_SO2 >ymax_pre_sn /2 width=2 by ylt_fwd_le_succ1/
+    | -HnW /3 width=7 by lift_inv_lref2_be, ylt_inj/
     ]
   | elim (lift_split … HVW i j) -HVW //
     #X #_ #H elim HnW -HnW //
@@ -44,13 +44,12 @@ lemma cpy_fwd_nlift2_ge: ∀G,L,U1,U2,l,m. ⦃G, L⦄ ⊢ U1 ▶[l, m] U2 →
     ]
   | #HnU2 elim (IHU12 … HnU2) -IHU12 -HnU2 -IHW12 /2 width=1 by yle_succ/
     [ /4 width=9 by nlift_bind_dx, or_introl/
-    | * #J #K #W #j #Hlj #Hji #HLK #HnW
-      elim (yle_inv_succ1 … Hlj) -Hlj #Hlj #Hj
-      lapply (ylt_O … Hj) -Hj #Hj
-      lapply (drop_inv_drop1_lt … HLK ?) // -HLK #HLK
-      >(plus_minus_m_m j 1) in ⊢ (%→?); [2: /3 width=3 by yle_trans, yle_inv_inj/ ]
-      #HnU1 <minus_le_minus_minus_comm in HnW;
-      /5 width=9 by nlift_bind_dx, monotonic_lt_pred, lt_plus_to_minus_r, ex5_4_intro, or_intror/
+    | * #J #K #W #j #Hlj elim (yle_inv_succ1 … Hlj) -Hlj #Hlj #Hj
+      <Hj >yminus_succ #Hji #HLK #HnW
+      lapply (drop_inv_drop1_lt … HLK ?) /2 width=1 by ylt_O/ -HLK #HLK
+      <yminus_SO2 in Hlj; #Hlj #H4
+      @or_intror @(ex5_4_intro … HLK) (**) (* explicit constructors *)
+      /3 width=9 by nlift_bind_dx, ylt_pred, ylt_inj/
     ]
   ]
 | #I #G #L #W1 #W2 #U1 #U2 #l #m #_ #_ #IHW12 #IHU12 #i #Hli #H elim (nlift_inv_flat … H) -H