update in basic_2 and apps_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 1ce29c009e4859aae2dbc6fc90045f0975c0782f..8d940a856aa7f28a1a3161d81a23367dab006352 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground_2/xoa/ex_2_3.ma".
 include "basic_2/notation/relations/predsubtystarproper_7.ma".
 include "basic_2/rt_transition/fpb.ma".
 include "basic_2/rt_computation/fpbs.ma".
@@ -19,39 +20,48 @@ include "basic_2/rt_computation/fpbs.ma".
 (* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
 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⦄.
+           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 G1 L1 T1 G2 L2 T2 = (fpbg h G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fpb_fpbg: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄ →
-                ⦃G1, L1, T1⦄ >[h] ⦃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,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⦄.
+      ❪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-.
 
+lemma fpbg_fqu_trans (h): ∀G1,G,G2,L1,L,L2,T1,T,T2.
+      ❪G1,L1,T1❫ >[h] ❪G,L,T❫ → ❪G,L,T❫ ⬂ ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
+/4 width=5 by fpbg_fpbq_trans, fpbq_fquq, fqu_fquq/
+qed-.
+
 (* Note: this is used in the closure proof *)
-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⦄.
+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,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-.
+lemma fpbg_feqx_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_feqx/ qed-.
 
 (* Properties with t-bound rt-transition for terms **************************)
 
-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. 
+lemma cpm_tneqx_cpm_fpbg (h) (G) (L):
+      ∀n1,T1,T. ❪G,L❫ ⊢ T1 ➡[h,n1] T → (T1 ≛ T → ⊥) →
+      ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 → ❪G,L,T1❫ >[h] ❪G,L,T2❫.
+/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.