- bug fix in the induction for the closure property

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / fpb.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpb.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpb.ma
index 06ff76ac9813f99dc1cae8b9417215f8cc10723c..94c114260e2e81099a71749ca68262ac181cd74a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpb.ma
@@ -13,17 +13,15 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/btpred_8.ma".
-include "basic_2/relocation/fsup.ma".
-include "basic_2/static/ssta.ma".
-include "basic_2/reduction/lpr.ma".
+include "basic_2/relocation/fquq_alt.ma".
+include "basic_2/reduction/lpx.ma".
 
 (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
 
 inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpb_fsup  : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
-| fpb_lpr   : ∀L2. ⦃G1, L1⦄ ⊢ ➡ L2 → fpb h g G1 L1 T1 G1 L2 T1
-| fpb_cpr   : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → fpb h g G1 L1 T1 G1 L1 T2
-| fpb_ssta  : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
+| fpb_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃⸮ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
+| fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
+| fpb_lpx : ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g] L2 → fpb h g G1 L1 T1 G1 L2 T1
 .
 
 interpretation
@@ -33,4 +31,10 @@ interpretation
 (* Basic properties *********************************************************)
 
 lemma fpb_refl: ∀h,g. tri_reflexive … (fpb h g).
-/2 width=1 by fpb_cpr/ qed.
+/2 width=1 by fpb_cpx/ qed.
+
+lemma cpr_fpb: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L, T1⦄ ≽[h, g] ⦃G, L, T2⦄. 
+/3 width=1 by fpb_cpx, cpr_cpx/ qed.
+
+lemma lpr_fpb: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1, T⦄ ≽[h, g] ⦃G, L2, T⦄.
+/3 width=1 by fpb_lpx, lpr_lpx/ qed.