Still a problem to be fixed: after reaching the border we must always add

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma
index d45a3c83fbebfa9fc9ab8050d9d5fe430d44de14..0a48ca02aaeef7a011475b4fbdad10b8d464bd20 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma
@@ -19,14 +19,12 @@ include "basic_2/relocation/fsup.ma".
 
 (* activate genv *)
 inductive fsupq: tri_relation genv lenv term ≝
-| fsupq_refl   : ∀G,L,T. fsupq G L T G L T
 | fsupq_lref_O : ∀I,G,L,V. fsupq G (L.ⓑ{I}V) (#0) G L V
 | fsupq_pair_sn: ∀I,G,L,V,T. fsupq G L (②{I}V.T) G L V
 | fsupq_bind_dx: ∀a,I,G,L,V,T. fsupq G L (ⓑ{a,I}V.T) G (L.ⓑ{I}V) T
 | fsupq_flat_dx: ∀I,G, L,V,T. fsupq G L (ⓕ{I}V.T) G L T
-| fsupq_ldrop  : ∀G1,G2,L1,K1,K2,T1,T2,U1,d,e.
-                 ⇩[d, e] L1 ≡ K1 → ⇧[d, e] T1 ≡ U1 →
-                 fsupq G1 K1 T1 G2 K2 T2 → fsupq G1 L1 U1 G2 K2 T2
+| fsupq_drop   : ∀G,L,K,T,U,e.
+                 ⇩[0, e] L ≡ K → ⇧[0, e] T ≡ U → fsupq G L U G K T
 .
 
 interpretation
@@ -35,36 +33,29 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma fsup_fsupq: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄.
-#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 // /2 width=7/ qed.
-
-(* Basic properties *********************************************************)
+lemma fsupq_refl: tri_reflexive … fsupq.
+/2 width=3 by fsupq_drop/ qed.
 
-lemma fsupq_lref_S_lt: ∀I,G1,G2,L,K,V,T,i.
-                       0 < i → ⦃G1, L, #(i-1)⦄ ⊃⸮ ⦃G2, K, T⦄ → ⦃G1, L.ⓑ{I}V, #i⦄ ⊃⸮ ⦃G2, K, T⦄.
-/3 width=7/ qed.
-
-lemma fsupq_lref: ∀I,G,K,V,i,L. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊃⸮ ⦃G, K, V⦄.
-/3 width=2/ qed.
+lemma fsup_fsupq: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄.
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 // /2 width=3 by fsupq_drop/
+qed.
 
 (* Basic forward lemmas *****************************************************)
 
 lemma fsupq_fwd_fw: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → ♯{G2, L2, T2} ≤ ♯{G1, L1, T1}.
-#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 // [1,2,3: /2 width=1/ ]
-#G1 #G2 #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
-@(transitive_le … IHT12) -IHT12 /2 width=1/
+#G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 /2 width=1 by lt_to_le/
+#G1 #L1 #K1 #T1 #U1 #e #HLK1 #HTU1
+lapply (ldrop_fwd_lw … HLK1) -HLK1
+lapply (lift_fwd_tw … HTU1) -HTU1
+/2 width=1 by le_plus, le_n/
 qed-.
 
 fact fsupq_fwd_length_lref1_aux: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
                                  ∀i. T1 = #i → |L2| ≤ |L1|.
 #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2 //
 [ #a #I #G #L #V #T #j #H destruct
-| #G1 #G2 #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
-  @(transitive_le … HLK1) /2 width=2/
+| #G1 #L1 #K1 #T1 #U1 #e #HLK1 #HTU1 #i #H destruct
+  /2 width=3 by ldrop_fwd_length_le4/
 ]
 qed-.