partial commit: just the components before "static" ...

[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..d45a3c83fbebfa9fc9ab8050d9d5fe430d44de14 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq.ma
@@ -12,21 +12,62 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/suptermopt_6.ma".
 include "basic_2/relocation/fsup.ma".
 
 (* OPTIONAL SUPCLOSURE ******************************************************)
 
-definition fsupq: bi_relation lenv term ≝ bi_RC … fsup.
+(* 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
+.
 
 interpretation
    "optional structural successor (closure)"
-   'SupTermOpt L1 T1 L2 T2 = (fsup L1 T1 L2 T2).
+   'SupTermOpt G1 L1 T1 G2 L2 T2 = (fsupq G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fsupq_refl: bi_reflexive … fsupq.
-/2 width=1/ 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=7/ qed.
 
-lemma fsup_fsupq: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄.
-/2 width=1/ qed.
+(* Basic properties *********************************************************)
+
+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.
+
+(* 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/
+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/
+]
+qed-.
 
+lemma fsupq_fwd_length_lref1: ∀G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊃⸮ ⦃G2, L2, T2⦄ → |L2| ≤ |L1|.
+/2 width=7 by fsupq_fwd_length_lref1_aux/
+qed-.