milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / fpbg.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
index bda560f425b152f8674c39ce778c325599d94cf6..1ce29c009e4859aae2dbc6fc90045f0975c0782f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
@@ -12,47 +12,46 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsubtystarproper_8.ma".
+include "basic_2/notation/relations/predsubtystarproper_7.ma".
 include "basic_2/rt_transition/fpb.ma".
 include "basic_2/rt_computation/fpbs.ma".
 
 (* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
-definition fpbg: ∀h. sd h → tri_relation genv lenv term ≝
-                 λh,o,G1,L1,T1,G2,L2,T2.
-                 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+definition fpbg: ∀h. tri_relation genv lenv term ≝
+                 λh,G1,L1,T1,G2,L2,T2.
+                 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h] ⦃G2, L2, T2⦄.
 
 interpretation "proper parallel rst-computation (closure)"
-   'PRedSubTyStarProper h o G1 L1 T1 G2 L2 T2 = (fpbg h o G1 L1 T1 G2 L2 T2).
+   'PRedSubTyStarProper h G1 L1 T1 G2 L2 T2 = (fpbg h G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fpb_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
-                ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
+lemma fpb_fpbg: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄ →
+                ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
 /2 width=5 by ex2_3_intro/ qed.
 
-lemma fpbg_fpbq_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                       ⦃G1, L1, T1⦄ >[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, o] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
+lemma fpbg_fpbq_trans: ∀h,G1,G,G2,L1,L,L2,T1,T,T2.
+                       ⦃G1, L1, T1⦄ >[h] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h] ⦃G2, L2, T2⦄ →
+                       ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
+#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
 /3 width=9 by fpbs_strap1, ex2_3_intro/
 qed-.
 
 (* Note: this is used in the closure proof *)
-lemma fpbg_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ >[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-#h #o #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
+lemma fpbg_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h] ⦃G2, L2, T2⦄ →
+                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ >[h] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
+#h #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
 qed-.
 
 (* Basic_2A1: uses: fpbg_fleq_trans *)
-lemma fpbg_fdeq_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >[h, o] ⦃G, L, T⦄ →
-                       ∀G2,L2,T2. ⦃G, L, T⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
+lemma fpbg_fdeq_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >[h] ⦃G, L, T⦄ →
+                       ∀G2,L2,T2. ⦃G, L, T⦄ ≛ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄.
 /3 width=5 by fpbg_fpbq_trans, fpbq_fdeq/ qed-.
 
 (* Properties with t-bound rt-transition for terms **************************)
 
-lemma cpm_tdneq_cpm_fpbg (h) (o) (G) (L):
-                         ∀n1,T1,T. ⦃G, L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛[h,o] T → ⊥) →
-                         ∀n2,T2. ⦃G, L⦄ ⊢ T ➡[n2,h] T2 →
-                         ⦃G, L, T1⦄ >[h,o] ⦃G, L, T2⦄.
+lemma cpm_tdneq_cpm_fpbg (h) (G) (L):
+                         ∀n1,T1,T. ⦃G, L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛ T → ⊥) →
+                         ∀n2,T2. ⦃G, L⦄ ⊢ T ➡[n2,h] T2 → ⦃G, L, T1⦄ >[h] ⦃G, L, T2⦄.
 /4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.