update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / fpb.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
index f0e7362b225704f5db6dc24b3b4da5edb9900ba9..5b0c68c2a6f563bcf0897e602ad61f5f96294023 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
@@ -12,30 +12,30 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/btpredproper_8.ma".
-include "basic_2/s_transition/fqu.ma".
-include "basic_2/static/lfdeq.ma".
-include "basic_2/rt_transition/lfpr_lfpx.ma".
+include "basic_2/notation/relations/predsubtyproper_7.ma".
+include "static_2/s_transition/fqu.ma".
+include "static_2/static/reqx.ma".
+include "basic_2/rt_transition/lpr_lpx.ma".
 
 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
 
-inductive fpb (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpb_fqu: â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 â\8a\90 â¦\83G2, L2, T2â¦\84 â\86\92 fpb h o G1 L1 T1 G2 L2 T2
-| fpb_cpx: â\88\80T2. â¦\83G1, L1â¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89¡[h, o] T2 â\86\92 â\8a¥) â\86\92 fpb h o G1 L1 T1 G1 L1 T2
-| fpb_lpx: â\88\80L2. â¦\83G1, L1â¦\84 â\8a¢ â¬\88[h, T1] L2 â\86\92 (L1 â\89¡[h, o, T1] L2 â\86\92 â\8a¥) â\86\92 fpb h o G1 L1 T1 G1 L2 T1
+inductive fpb (h) (G1) (L1) (T1): relation3 genv lenv term ≝
+| fpb_fqu: â\88\80G2,L2,T2. â\9dªG1,L1,T1â\9d« â¬\82 â\9dªG2,L2,T2â\9d« â\86\92 fpb h G1 L1 T1 G2 L2 T2
+| fpb_cpx: â\88\80T2. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88[h] T2 â\86\92 (T1 â\89\9b T2 â\86\92 â\8a¥) â\86\92 fpb h G1 L1 T1 G1 L1 T2
+| fpb_lpx: â\88\80L2. â\9dªG1,L1â\9d« â\8a¢ â¬\88[h] L2 â\86\92 (L1 â\89\9b[T1] L2 â\86\92 â\8a¥) â\86\92 fpb h G1 L1 T1 G1 L2 T1
 .
 
 interpretation
    "proper parallel rst-transition (closure)"
-   'BTPRedProper h o G1 L1 T1 G2 L2 T2 = (fpb h o G1 L1 T1 G2 L2 T2).
+   'PRedSubTyProper h G1 L1 T1 G2 L2 T2 = (fpb h G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: includes: cpr_fpb *)
-lemma cpm_fpb: ∀n,h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → (T1 ≡[h, o] T2 → ⊥) →
-               ⦃G, L, T1⦄ ≻[h, o] ⦃G, L, T2⦄.
+lemma cpm_fpb (n) (h) (G) (L): ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[n,h] T2 → (T1 ≛ T2 → ⊥) →
+                                   ❪G,L,T1❫ ≻[h] ❪G,L,T2❫.
 /3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
 
-lemma lpr_fpb: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → (L1 ≡[h, o, T] L2 → ⊥) →
-               ⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄.
-/3 width=1 by fpb_lpx, lfpr_fwd_lfpx/ qed.
+lemma lpr_fpb (h) (G) (T): ∀L1,L2. ❪G,L1❫ ⊢ ➡[h] L2 → (L1 ≛[T] L2 → ⊥) →
+                           ❪G,L1,T❫ ≻[h] ❪G,L2,T❫.
+/3 width=1 by fpb_lpx, lpr_fwd_lpx/ qed.