update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma
index ac20a62590676f2533fb981b5180aee77996dfcb..0ec2597f1e3ca71c3156f4df3dea8b8b55b9d813 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq_fpb.ma
@@ -12,44 +12,44 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/fpb_ffdeq.ma".
+include "basic_2/rt_transition/fpb_feqx.ma".
 include "basic_2/rt_transition/fpbq.ma".
 
 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
 
 (* Properties with proper parallel rst-transition for closures **************)
 
-lemma fpb_fpbq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
-                â¦\83G1, L1, T1â¦\84 â\89½[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
-/3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lfpx, fqu_fquq/
+lemma fpb_fpbq: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ →
+                â\9dªG1,L1,T1â\9d« â\89½[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/3 width=1 by fpbq_fquq, fpbq_cpx, fpbq_lpx, fqu_fquq/
 qed.
 
 (* Basic_2A1: fpb_fpbq_alt *)
-lemma fpb_fpbq_ffdneq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
-                       â\88§â\88§ â¦\83G1, L1, T1â¦\84 â\89½[h, o] â¦\83G2, L2, T2â¦\84 & (â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] â¦\83G2, L2, T2â¦\84 → ⊥).
-/3 width=10 by fpb_fpbq, fpb_inv_ffdeq, conj/ qed-.
+lemma fpb_fpbq_fneqx: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ →
+                       â\88§â\88§ â\9dªG1,L1,T1â\9d« â\89½[h] â\9dªG2,L2,T2â\9d« & (â\9dªG1,L1,T1â\9d« â\89\9b â\9dªG2,L2,T2â\9d« → ⊥).
+/3 width=10 by fpb_fpbq, fpb_inv_feqx, conj/ qed-.
 
 (* Inversrion lemmas with proper parallel rst-transition for closures *******)
 
 (* Basic_2A1: uses: fpbq_ind_alt *)
-lemma fpbq_inv_fpb: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ →
-                    â\88¨â\88¨ â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] â¦\83G2, L2, T2â¦\84
-                     | â¦\83G1, L1, T1â¦\84 â\89»[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+lemma fpbq_inv_fpb: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽[h] ❪G2,L2,T2❫ →
+                    â\88¨â\88¨ â\9dªG1,L1,T1â\9d« â\89\9b â\9dªG2,L2,T2â\9d«
+                     | â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
 [ #G2 #L2 #T2 * [2: * #H1 #H2 #H3 destruct ]
-  /3 width=1 by fpb_fqu, ffdeq_intro_sn, or_intror, or_introl/
-| #T2 #H elim (tdeq_dec h o T1 T2)
-  /4 width=1 by fpb_cpx, ffdeq_intro_sn, or_intror, or_introl/
-| #L2 elim (lfdeq_dec h o L1 L2 T1)
-  /4 width=1 by fpb_lfpx, ffdeq_intro_sn, or_intror, or_introl/
+  /3 width=1 by fpb_fqu, feqx_intro_sn, or_intror, or_introl/
+| #T2 #H elim (teqx_dec T1 T2)
+  /4 width=1 by fpb_cpx, feqx_intro_sn, or_intror, or_introl/
+| #L2 elim (reqx_dec L1 L2 T1)
+  /4 width=1 by fpb_lpx, feqx_intro_sn, or_intror, or_introl/
 | /2 width=1 by or_introl/
 ]
 qed-.
 
 (* Basic_2A1: fpbq_inv_fpb_alt *)
-lemma fpbq_ffdneq_inv_fpb: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ →
-                           (â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â\8a¥) â\86\92 â¦\83G1, L1, T1â¦\84 â\89»[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #H0
+lemma fpbq_fneqx_inv_fpb: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽[h] ❪G2,L2,T2❫ →
+                           (â\9dªG1,L1,T1â\9d« â\89\9b â\9dªG2,L2,T2â\9d« â\86\92 â\8a¥) â\86\92 â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G2 #L1 #L2 #T1 #T2 #H #H0
 elim (fpbq_inv_fpb … H) -H // #H elim H0 -H0 //
 qed-.