- advances in the theory of cofrees

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fleq.ma
index 826500bf1b80affa27e01fdf9e13ded85a93eae1..9f0c8d41522f6c7fde6ff5cac3864eb3e6e805d6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_fleq.ma
@@ -12,25 +12,14 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/reduction/fpbc.ma".
-include "basic_2/computation/fleq.ma".
-include "basic_2/computation/fpbs_alt.ma".
+include "basic_2/substitution/fleq.ma".
+include "basic_2/computation/fpbs.ma".
 
 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
 
-(* Forward lemmas on equivalent "big tree" normal forms *********************)
+(* Properties on lazy equivalence on closures *******************************)
 
-lemma fpbs_fwd_fpb_sn: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ ⋕[h, g] ⦃G2, L2, T2⦄ ∨
-                       ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim(fpbs_fpbsa … H) -H
-#L #T #HT1 #HT2 #HL2 elim (eq_term_dec T1 T) #H destruct
-[ -HT1 elim (fqus_inv_gen … HT2) -HT2
-  [ #HT2 elim (fqup_inv_step_sn … HT2) -HT2
-    /5 width=9 by fpbsa_inv_fpbs, fpbc_fqu, ex3_2_intro, ex2_3_intro, or_intror/
-  | * #HG #HL #HT destruct /3 width=1 by and3_intro, or_introl/
-  ]
-| elim (cpxs_neq_inv_step_sn … HT1 H) -HT1 -H
-  /5 width=9 by fpbsa_inv_fpbs, fpbc_cpx, ex3_2_intro, ex2_3_intro, or_intror/
-]
-qed-.
+lemma fleq_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2.
+                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * /2 width=1 by lleq_fpbs/
+qed.