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

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / fsups.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/fsups.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/fsups.ma
index d71d52fbf014ac203a7c406ac17bebcf347dc838..51126ebd102247cf3cae9015ac84fd8bf7512601 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/fsups.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/fsups.ma
@@ -12,72 +12,72 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/suptermstar_4.ma".
+include "basic_2/notation/relations/suptermstar_6.ma".
 include "basic_2/relocation/fsupq.ma".
 
 (* STAR-ITERATED SUPCLOSURE *************************************************)
 
-definition fsups: bi_relation lenv term ≝ bi_TC … fsupq.
+definition fsups: tri_relation genv lenv term ≝ tri_TC … fsupq.
 
 interpretation "star-iterated structural successor (closure)"
-   'SupTermStar L1 T1 L2 T2 = (fsups L1 T1 L2 T2).
+   'SupTermStar G1 L1 T1 G2 L2 T2 = (fsups G1 L1 T1 G2 L2 T2).
 
 (* Basic eliminators ********************************************************)
 
-lemma fsups_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
-                 (∀L,L2,T,T2. ⦃L1, T1⦄ ⊃* ⦃L, T⦄ → ⦃L, T⦄ ⊃⸮ ⦃L2, T2⦄ → R L T → R L2 T2) →
-                 ∀L2,T2. ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄ → R L2 T2.
-#L1 #T1 #R #IH1 #IH2 #L2 #T2 #H
-@(bi_TC_star_ind … IH1 IH2 ? ? H) //
+lemma fsups_ind: ∀G1,L1,T1. ∀R:relation3 …. R G1 L1 T1 →
+                 (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃⸮ ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
+                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → R G2 L2 T2.
+#G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
+@(tri_TC_star_ind … IH1 IH2 G2 L2 T2 H) //
 qed-.
 
-lemma fsups_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
-                    (∀L1,L,T1,T. ⦃L1, T1⦄ ⊃⸮ ⦃L, T⦄ → ⦃L, T⦄ ⊃* ⦃L2, T2⦄ → R L T → R L1 T1) →
-                    ∀L1,T1. ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄ → R L1 T1.
-#L2 #T2 #R #IH1 #IH2 #L1 #T1 #H
-@(bi_TC_star_ind_dx … IH1 IH2 ? ? H) //
+lemma fsups_ind_dx: ∀G2,L2,T2. ∀R:relation3 …. R G2 L2 T2 →
+                    (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃* ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
+                    ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄ → R G1 L1 T1.
+#G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
+@(tri_TC_star_ind_dx … IH1 IH2 G1 L1 T1 H) //
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma fsups_refl: bi_reflexive … fsups.
+lemma fsups_refl: tri_reflexive … fsups.
 /2 width=1/ qed.
 
-lemma fsupq_fsups: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄.
+lemma fsupq_fsups: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
 /2 width=1/ qed.
 
-lemma fsups_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃* ⦃L, T⦄ → ⦃L, T⦄ ⊃⸮ ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄.
-/2 width=4/ qed.
+lemma fsups_strap1: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃* ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃⸮ ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
+/2 width=5/ qed.
 
-lemma fsups_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃⸮ ⦃L, T⦄ → ⦃L, T⦄ ⊃* ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄.
-/2 width=4/ qed.
+lemma fsups_strap2: ∀G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊃* ⦃G2, L2, T2⦄ →
+                    ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
+/2 width=5/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma fsups_fwd_fw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄ → ♯{L2, T2} ≤ ♯{L1, T1}.
-#L1 #L2 #T1 #T2 #H @(fsups_ind … H) -L2 -T2 //
+lemma fsups_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 @(fsups_ind … H) -L2 -T2 //
 /3 width=3 by fsupq_fwd_fw, transitive_le/ (**) (* slow even with trace *)
 qed-.
 (*
 (* Advanced inversion lemmas on plus-iterated supclosure ********************)
 
-lamma fsupp_inv_bind1_fsups: ∀b,J,L1,L2,W,U,T2. ⦃L1, ⓑ{b,J}W.U⦄ ⊃+ ⦃L2, T2⦄ →
-                             ⦃L1, W⦄ ⊃* ⦃L2, T2⦄ ∨ ⦃L1.ⓑ{J}W, U⦄ ⊃* ⦃L2, T2⦄.
-#b #J #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -L2 -T2
-[ #L2 #T2 #H
-  elim (fsup_inv_bind1 … H) -H * #H1 #H2 destruct /2 width=1/
-| #L #T #L2 #T2 #_ #HT2 * /3 width=4/
+lamma fsupp_inv_bind1_fsups: ∀b,J,G1,G2,L1,L2,W,U,T2. ⦃G1, L1, ⓑ{b,J}W.U⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                             ⦃G1, L1, W⦄ ⊃* ⦃G2, L2, T2⦄ ∨ ⦃L1.ⓑ{J}W, U⦄ ⊃* ⦃G2, L2, T2⦄.
+#b #J #G1 #G2 #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -G2 -L2 -T2
+[ #G2 #L2 #T2 #H
+  elim (fsup_inv_bind1 … H) -H * #H1 #H2 #H3 destruct /2 width=1/
+| #G #G2 #L #L2 #T #T2 #_ #HT2 * /3 width=4/
 ]
 qad-.
 
-lamma fsupp_inv_flat1_fsups: ∀J,L1,L2,W,U,T2. ⦃L1, ⓕ{J}W.U⦄ ⊃+ ⦃L2, T2⦄ →
-                             ⦃L1, W⦄ ⊃* ⦃L2, T2⦄ ∨ ⦃L1, U⦄ ⊃* ⦃L2, T2⦄.
-#J #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -L2 -T2
-[ #L2 #T2 #H
+lamma fsupp_inv_flat1_fsups: ∀J,G1,G2,L1,L2,W,U,T2. ⦃G1, L1, ⓕ{J}W.U⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                             ⦃G1, L1, W⦄ ⊃* ⦃G2, L2, T2⦄ ∨ ⦃G1, L1, U⦄ ⊃* ⦃G2, L2, T2⦄.
+#J #G1 #G2 #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -G2 -L2 -T2
+[ #G2 #L2 #T2 #H
   elim (fsup_inv_flat1 … H) -H #H1 * #H2 destruct /2 width=1/
-| #L #T #L2 #T2 #_ #HT2 * /3 width=4/
+| #G #G2 #L #L2 #T #T2 #_ #HT2 * /3 width=4/
 ]
 qad-.
 *)