lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / fsup.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
index d10d9d28b358c01bb69c13967d4c7a811f69cb59..53f7b55840a5a76d99d81fb480e96e0ffd43e585 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/supterm_4.ma".
 include "basic_2/grammar/cl_weight.ma".
 include "basic_2/relocation/ldrop.ma".
 
@@ -23,7 +24,7 @@ inductive fsup: bi_relation lenv term ≝
 | fsup_bind_dx : ∀a,I,L,V,T. fsup L (ⓑ{a,I}V.T) (L.ⓑ{I}V) T
 | fsup_flat_dx : ∀I,L,V,T.   fsup L (ⓕ{I}V.T) L T
 | fsup_ldrop_lt: ∀L,K,T,U,d,e.
-                 ⇩[d, e] L ≡ K → ⇧[d, e] T ≡ U → |K| < |L| → fsup L U K T
+                 ⇩[d, e] L ≡ K → ⇧[d, e] T ≡ U → 0 < e → fsup L U K T
 | fsup_ldrop   : ∀L1,K1,K2,T1,T2,U1,d,e.
                  ⇩[d, e] L1 ≡ K1 → ⇧[d, e] T1 ≡ U1 →
                  fsup K1 T1 K2 T2 → fsup L1 U1 K2 T2
@@ -36,7 +37,8 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma fsup_lref_S_lt: ∀I,L,K,V,T,i. 0 < i → ⦃L, #(i-1)⦄ ⊃ ⦃K, T⦄ → ⦃L.ⓑ{I}V, #i⦄ ⊃ ⦃K, T⦄.
-/3 width=7/ qed.
+#I #L #K #V #T #i #Hi #H /3 width=7 by fsup_ldrop, ldrop_ldrop, lift_lref_ge_minus/ (**) (* auto too slow without trace *)
+qed.
 
 lemma fsup_lref: ∀I,K,V,i,L. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃L, #i⦄ ⊃ ⦃K, V⦄.
 #I #K #V #i @(nat_elim1 i) -i #i #IH #L #H
@@ -65,10 +67,11 @@ qed-.
 fact fsup_fwd_length_lref1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
                                 ∀i. T1 = #i → |L2| < |L1|.
 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2
-[1,5:  normalize //
+[1: normalize //
 |3: #a
+|5: /2 width=4 by ldrop_fwd_length_lt4/
 |6: #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #i #H destruct
-    lapply (ldrop_fwd_length … HLK1) -HLK1 #HLK1
+    lapply (ldrop_fwd_length_le4 … HLK1) -HLK1 #HLK1
     elim (lift_inv_lref2 … HTU1) -HTU1 * #Hdei #H destruct
     @(lt_to_le_to_lt … HLK1) /2 width=2/
 ] #I #L #V #T #j #H destruct