milestone update in basic_2, update in ground and static_2

[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 1fa7b7209b12254bdd1a0b9b6c91f426e9a023e1..e49faa0eb0845f8a6a2f77200039fb4966a369f2 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 +12,48 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/fpb_fdeq.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
+lemma fpb_fpbq:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
+#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_fdeq, conj/ qed-.
+lemma fpb_fpbq_fneqx:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
+      ∧∧ ❪G1,L1,T1❫ ≽ ❪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:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
+      ∨∨ ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫
+       | ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
 [ #G2 #L2 #T2 * [2: * #H1 #H2 #H3 destruct ]
-  /3 width=1 by fpb_fqu, fdeq_intro_sn, or_intror, or_introl/
-| #T2 #H elim (tdeq_dec h o T1 T2)
-  /4 width=1 by fpb_cpx, fdeq_intro_sn, or_intror, or_introl/
-| #L2 elim (rdeq_dec h o L1 L2 T1)
-  /4 width=1 by fpb_lpx, fdeq_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:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
+      (❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → ⊥) → ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T2 #H #H0
 elim (fpbq_inv_fpb … H) -H // #H elim H0 -H0 //
 qed-.