- fpbg can be reflexive (example given)

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
index 293e666d528866c8a6f83a05c3b3b3c8dc8dad93..754811ec29ab02336d54fe6ead5048b1fa47473b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fleq.ma
@@ -12,10 +12,10 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbc_fleq.ma".
+include "basic_2/reduction/fpbc_fleq.ma".
 include "basic_2/computation/fpbg.ma".
 
-(* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
+(* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
 
 (* Properties on lazy equivalence for closures ******************************)
 
@@ -34,45 +34,3 @@ lemma fleq_fpbg_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2
 | /4 width=9 by fpbg_strap2, fleq_fpbc_trans/
 ]
 qed-.
-
-lemma fpbs_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                 ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨
-                 ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
-[ /2 width=1 by or_introl/
-| #G #G2 #L #L2 #T #T2 #_ #H2 * #H1 elim (fpb_fpbu … H2) -H2 #H2
-  [ /3 width=5 by fleq_trans, or_introl/
-  | /5 width=5 by fpbc_fpbg, fleq_fpbc_trans, fpbu_fpbc, or_intror/
-  | /3 width=5 by fpbg_fleq_trans, or_intror/
-  | /4 width=5 by fpbg_strap1, fpbu_fpbc, or_intror/
-  ]
-]
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma fpbg_fpb_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
-                      ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fpb_fpbu … H2) -H2
-/3 width=5 by fpbg_fleq_trans, fpbg_strap1, fpbu_fpbc/
-qed-.
-
-
-lemma fpb_fpbg_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
-                      ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 elim (fpb_fpbu … H1) -H1
-/3 width=5 by fleq_fpbg_trans, fpbg_strap2, fpbu_fpbc/
-qed-.
-
-lemma fpbs_fpbg_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
-                       ∀G2,L2,T2. ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpb_fpbg_trans/
-qed-.
-
-(* Note: this is used in the closure proof *)
-lemma fpbg_fpbs_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
-                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpb_trans/
-qed-.