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[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 9400a84d76954d5eb7da382e92dd44cd202b9c5e..4c40afe091f81167218c0907dd293093e3288e91 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma
@@ -12,21 +12,60 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/suptermopt_4.ma".
 include "basic_2/relocation/fsup.ma".
 
 (* OPTIONAL SUPCLOSURE ******************************************************)
 
-definition fsupq: bi_relation lenv term ≝ bi_RC … fsup.
+inductive fsupq: bi_relation lenv term ≝
+| fsupq_refl   : ∀L,T. fsupq L T L T
+| fsupq_lref_O : ∀I,L,V. fsupq (L.ⓑ{I}V) (#0) L V
+| fsupq_pair_sn: ∀I,L,V,T. fsupq L (②{I}V.T) L V
+| fsupq_bind_dx: ∀a,I,L,V,T. fsupq L (ⓑ{a,I}V.T) (L.ⓑ{I}V) T
+| fsupq_flat_dx: ∀I,L,V,T.   fsupq L (ⓕ{I}V.T) L T
+| fsupq_ldrop  : ∀L1,K1,K2,T1,T2,U1,d,e.
+                ⇩[d, e] L1 ≡ K1 → ⇧[d, e] T1 ≡ U1 →
+                fsupq K1 T1 K2 T2 → fsupq L1 U1 K2 T2
+.
 
 interpretation
    "optional structural successor (closure)"
-   'SupTermOpt L1 T1 L2 T2 = (fsup L1 T1 L2 T2).
+   'SupTermOpt L1 T1 L2 T2 = (fsupq L1 T1 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fsupq_refl: bi_reflexive … fsupq.
-/2 width=1/ qed.
-
 lemma fsup_fsupq: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄.
-/2 width=1/ qed.
+#L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 // /2 width=7/ qed.
+
+(* Basic properties *********************************************************)
+
+lemma fsupq_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.
+
+lemma fsupq_lref: ∀I,K,V,i,L. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃L, #i⦄ ⊃⸮ ⦃K, V⦄.
+/3 width=2/ qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma fsupq_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 // [1,2,3: /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
+@(transitive_le … IHT12) -IHT12 /2 width=1/
+qed-.
+
+fact fsupq_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 //
+[ #a #I #L #V #T #j #H destruct
+| #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/
+]
+qed-.
 
+lemma fsupq_fwd_length_lref1: ∀L1,L2,T2,i. ⦃L1, #i⦄ ⊃⸮ ⦃L2, T2⦄ → |L2| ≤ |L1|.
+/2 width=5 by fsupq_fwd_length_lref1_aux/
+qed-.