- advances in the theory of cofrees

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / fpbc.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc.ma
index a66e1ac90bee5a1f8e0d141989bffc2351c0ee36..82ea6ec0f5c0c1bc9b77b6b331888ca2ba6fd8f1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc.ma
@@ -12,36 +12,22 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/btpredproper_8.ma".
-include "basic_2/relocation/lleq.ma".
-include "basic_2/computation/fpbs.ma".
+include "basic_2/notation/relations/lazybtpredproper_8.ma".
+include "basic_2/substitution/fleq.ma".
+include "basic_2/computation/fpbu.ma".
 
-(* ATOMIC "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************)
+(* SINGLE-STEP "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********)
 
-inductive fpbc (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpbc_fqup: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → fpbc h g G1 L1 T1 G2 L2 T2
-| fpbc_cpxs: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → fpbc h g G1 L1 T1 G1 L1 T2
-| fpbc_lpxs: ∀L2. ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ⋕[0, T1] L2 → ⊥) → fpbc h g G1 L1 T1 G1 L2 T1
-.
+definition fpbc: ∀h. sd h → tri_relation genv lenv term ≝
+                 λh,g,G1,L1,T1,G2,L2,T2.
+                 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≡[0] ⦃G2, L2, T2⦄.
 
 interpretation
-   "'big tree' proper parallel reduction (closure)"
-   'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbc h g G1 L1 T1 G2 L2 T2).
+   "single-step 'big tree' proper parallel reduction (closure)"
+   'LazyBTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbc h g G1 L1 T1 G2 L2 T2).
 
-(* Basic properties *********************************************************)
+(* Baic properties **********************************************************)
 
-lemma cprs_fpbc: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
-                 ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
-/3 width=1 by fpbc_cpxs, cprs_cpxs/ qed.
-
-lemma lprs_fpbc: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → (L1 ⋕[0, T] L2 → ⊥) →
-                 ⦃G, L1, T⦄ ≻[h, g] ⦃G, L2, T⦄.
-/3 width=1 by fpbc_lpxs, lprs_lpxs/ qed.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma fpbc_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
-                     ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
-/3 width=1 by lpxs_fpbs, cpxs_fpbs, fqup_fpbs/
-qed-.
+lemma fpbu_fpbc: ∀h,g,G1,G2,L1,L2,T1,T2.
+                 ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄.
+/2 width=5 by ex2_3_intro/ qed.