- new component "s_transition" for the restored fqu and fquq

[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 efe7c5e3d7963a8a70463f161c5b0bb43c9b97ad..cce7d39ffeaf44fd98b3e83153a2b6de92861858 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/fpb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/fpb.ma
@@ -12,31 +12,29 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/btpred_8.ma".
-include "basic_2/substitution/fquq.ma".
+include "basic_2/notation/relations/btpredproper_8.ma".
+include "basic_2/substitution/fqu.ma".
 include "basic_2/multiple/lleq.ma".
 include "basic_2/reduction/lpx.ma".
 
-(* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
+(* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
 
-inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| 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
-| fpb_lleq: ∀L2. L1 ≡[T1, 0] L2 → fpb h g G1 L1 T1 G1 L2 T1
+inductive fpb (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝
+| fpb_fqu: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h o G1 L1 T1 G2 L2 T2
+| fpb_cpx: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, o] T2 → (T1 = T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2
+| fpb_lpx: ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, o] L2 → (L1 ≡[T1, 0] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1
 .
 
 interpretation
-   "'big tree' parallel reduction (closure)"
-   'BTPRed h g G1 L1 T1 G2 L2 T2 = (fpb h g G1 L1 T1 G2 L2 T2).
+   "'rst' proper parallel reduction (closure)"
+   'BTPRedProper h o G1 L1 T1 G2 L2 T2 = (fpb h o G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fpb_refl: ∀h,g. tri_reflexive … (fpb h g).
-/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⦄. 
+lemma cpr_fpb: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) →
+               ⦃G, L, T1⦄ ≻[h, o] ⦃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⦄.
+lemma lpr_fpb: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → (L1 ≡[T, 0] L2 → ⊥) →
+               ⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄.
 /3 width=1 by fpb_lpx, lpr_lpx/ qed.