- advances in the theory of cofrees

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbu.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbu.ma
index 52c00a82befddc9bdc9ee83f004b8782896ae7cb..1525567aa4e3904178c69441a3be0ce077df6815 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbu.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbu.ma
@@ -13,15 +13,14 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/btpredproper_8.ma".
-include "basic_2/substitution/lleq.ma".
 include "basic_2/computation/fpbs.ma".
 
 (* UNITARY "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **************)
 
 inductive fpbu (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpbu_fqup : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → fpbu h g G1 L1 T1 G2 L2 T2
-| fpbu_cpxs : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → fpbu h g G1 L1 T1 G1 L1 T2
-| fpbu_llpxs: ∀L2. ⦃G1, L1⦄ ⊢ ➡*[h, g, T1, 0] L2 → (L1 ⋕[T1, 0] L2 → ⊥) → fpbu h g G1 L1 T1 G1 L2 T1
+| fpbu_fqup: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → fpbu h g G1 L1 T1 G2 L2 T2
+| fpbu_cpxs: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → fpbu h g G1 L1 T1 G1 L1 T2
+| fpbu_lpxs: ∀L2. ⦃G1, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ≡[T1, 0] L2 → ⊥) → fpbu h g G1 L1 T1 G1 L2 T1
 .
 
 interpretation
@@ -34,14 +33,14 @@ lemma cprs_fpbu: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → 
                  ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
 /3 width=1 by fpbu_cpxs, cprs_cpxs/ qed.
 
-lemma llprs_fpbu: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡*[T, 0] L2 → (L1 ⋕[T, 0] L2 → ⊥) →
-                  ⦃G, L1, T⦄ ≻[h, g] ⦃G, L2, T⦄.
-/3 width=1 by fpbu_llpxs, llprs_llpxs/ qed.
+lemma lprs_fpbu: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → (L1 ≡[T, 0] L2 → ⊥) →
+                 ⦃G, L1, T⦄ ≻[h, g] ⦃G, L2, T⦄.
+/3 width=1 by fpbu_lpxs, lprs_lpxs/ qed.
 
 (* Basic forward lemmas *****************************************************)
 
 lemma fpbu_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 llpxs_fpbs, cpxs_fpbs, fqup_fpbs/
+/3 width=1 by lpxs_fpbs, cpxs_fpbs, fqup_fpbs/
 qed-.