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 16fbeb12889085acebf415913168798d752398c6..53f7b55840a5a76d99d81fb480e96e0ffd43e585 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsup.ma
@@ -12,19 +12,22 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/supterm_4.ma".
 include "basic_2/grammar/cl_weight.ma".
 include "basic_2/relocation/ldrop.ma".
 
 (* SUPCLOSURE ***************************************************************)
 
 inductive fsup: bi_relation lenv term ≝
-| fsup_lref   : ∀I,L,V. fsup (L.ⓑ{I}V) (#0) L V
-| fsup_pair_sn: ∀I,L,V,T. fsup L (②{I}V.T) L V
-| 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  : ∀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
+| fsup_lref_O  : ∀I,L,V. fsup (L.ⓑ{I}V) (#0) L V
+| fsup_pair_sn : ∀I,L,V,T. fsup L (②{I}V.T) L V
+| 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 → 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
 .
 
 interpretation
@@ -34,7 +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
@@ -49,19 +53,27 @@ qed.
 
 lemma fsup_fwd_fw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ♯{L2, T2} < ♯{L1, T1}.
 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 //
-#L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12
-lapply (ldrop_fwd_lw … HLK1) -HLK1 #HLK1
-lapply (lift_fwd_tw … HTU1) -HTU1 #HTU1
-@(lt_to_le_to_lt … IHT12) -IHT12 /2 width=1/
+[ #L #K #T #U #d #e #HLK #HTU #HKL
+  lapply (ldrop_fwd_lw_lt … HLK HKL) -HKL -HLK #HKL
+  lapply (lift_fwd_tw … HTU) -d -e #H
+  normalize in ⊢ (?%%); /2 width=1/
+| #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12
+  lapply (ldrop_fwd_lw … HLK1) -HLK1 #HLK1
+  lapply (lift_fwd_tw … HTU1) -HTU1 #HTU1
+  @(lt_to_le_to_lt … IHT12) -IHT12 /2 width=1/
+]
 qed-.
 
-fact fsup_fwd_length_lref1_aux: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ∀i. T1 = #i → |L2| < |L1|.
+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
-[5: #L1 #K1 #K2 #T1 #T2 #U1 #d #e #HLK1 #HTU1 #_ #IHT12 #i #H destruct
-    lapply (ldrop_fwd_length … HLK1) -HLK1 #HLK1
+[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_le4 … HLK1) -HLK1 #HLK1
     elim (lift_inv_lref2 … HTU1) -HTU1 * #Hdei #H destruct
     @(lt_to_le_to_lt … HLK1) /2 width=2/
-| normalize // |3: #a
 ] #I #L #V #T #j #H destruct
 qed-.