X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Ffpbq_fpb.ma;h=0ec2597f1e3ca71c3156f4df3dea8b8b55b9d813;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=ac20a62590676f2533fb981b5180aee77996dfcb;hpb=c6305166703a17801bbd08a85fe93ef4abf8ff85;p=helm.git

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 ac20a6259..0ec2597f1 100644
--- 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⦄ →
-                ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄.
-#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❫ →
+                ❪G1,L1,T1❫ ≽[h] ❪G2,L2,T2❫.
+#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⦄ →
-                       ∧∧ ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ & (⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥).
-/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❫ →
+                       ∧∧ ❪G1,L1,T1❫ ≽[h] ❪G2,L2,T2❫ & (❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → ⊥).
+/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⦄ →
-                    ∨∨ ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄
-                     | ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄.
-#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❫ →
+                    ∨∨ ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫
+                     | ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫.
+#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⦄ →
-                           (⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥) → ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄.
-#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❫ →
+                           (❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → ⊥) → ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫.
+#h #G1 #G2 #L1 #L2 #T1 #T2 #H #H0
 elim (fpbq_inv_fpb … H) -H // #H elim H0 -H0 //
 qed-.