milestone update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / fpbg_fpbs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
index 3641326f8177364d577bedc2f4d0e964177c08cf..a1ac691824c89bc946a8a9fc477a1f216c2cc6f1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
@@ -12,83 +12,35 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/static/fdeq_fqup.ma".
-include "static_2/static/fdeq_fdeq.ma".
-include "basic_2/rt_transition/fpbq_fpb.ma".
+include "basic_2/rt_computation/fpbs_fpbs.ma".
 include "basic_2/rt_computation/fpbg.ma".
 
 (* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
 (* Advanced forward lemmas **************************************************)
 
-lemma fpbg_fwd_fpbs: ∀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 *
-/3 width=5 by fpbs_strap2, fpb_fpbq/
+lemma fpbg_fwd_fpbs (G1) (G2) (L1) (L2) (T1) (T2):
+      ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T2 #H
+elim (fpbg_inv_gen … H) -H
+/4 width=9 by fpbs_trans, fpbs_strap2, fpbc_fwd_fpb/
 qed-.
 
-(* Advanced properties with degree-based equivalence on closures ************)
+(* Advanced properties ******************************************************)
 
-(* Basic_2A1: uses: fleq_fpbg_trans *)
-lemma fdeq_fpbg_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
-                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-#h #o #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
-elim (fdeq_fpb_trans …  H1 … H0) -G -L -T
-/4 width=9 by fpbs_strap2, fpbq_fdeq, ex2_3_intro/
+lemma fpbs_fpbg_trans (G) (L) (T):
+      ∀G1,L1,T1. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+#G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
+elim (fpbg_inv_gen … H2) -H2
+/3 width=13 by fpbg_intro, fpbs_trans/
 qed-.
 
-(* Properties with parallel proper rst-reduction on closures ****************)
-
-lemma fpb_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                      ⦃G1, L1, T1⦄ ≻[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
-                      ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-/3 width=5 by fpbg_fwd_fpbs, ex2_3_intro/ qed-.
-
-(* Properties with parallel rst-reduction on closures ***********************)
-
-lemma fpbq_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                       ⦃G1, L1, T1⦄ ≽[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
-elim (fpbq_inv_fpb … H1) -H1
-/2 width=5 by fdeq_fpbg_trans, fpb_fpbg_trans/
-qed-.
-
-(* Properties with parallel rst-compuutation on closures ********************)
-
-lemma fpbs_fpbg_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                       ∀G2,L2,T2. ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpbq_fpbg_trans/
-qed-.
-
-(* Advanced inversion lemmas of parallel rst-computation on closures ********)
-
-(* Basic_2A1: was: fpbs_fpbg *)
-lemma fpbs_inv_fpbg: ∀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 @(fpbs_ind … H) -G2 -L2 -T2
-[ /2 width=1 by or_introl/
-| #G #G2 #L #L2 #T #T2 #_ #H2 * #H1
-  elim (fpbq_inv_fpb … H2) -H2 #H2
-  [ /3 width=5 by fdeq_trans, or_introl/
-  | elim (fdeq_fpb_trans … H1 … H2) -G -L -T
-    /4 width=5 by ex2_3_intro, or_intror, fdeq_fpbs/
-  | /3 width=5 by fpbg_fdeq_trans, or_intror/
-  | /4 width=5 by fpbg_fpbq_trans, fpb_fpbq, or_intror/
-  ]
-]
-qed-.
-
-(* Advanced properties of parallel rst-computation on closures **************)
-
-lemma fpbs_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≥[h, o] ⦃F2, K2, T2⦄ →
-                      ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
-                      ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≥[h, o] ⦃G2, L2, U2⦄.
-#h #o #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_inv_fpbg … H) -H
-[ #H12 #G2 #L2 #U2 #H2 elim (fdeq_fpb_trans … H12 … H2) -F2 -K2 -T2
-  /3 width=5 by fdeq_fpbs, ex2_3_intro/
-| * #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9
-  @(ex2_3_intro … H4) -H4 /3 width=5 by fpbs_strap1, fpb_fpbq/
-]
+(* Note: this is used in the closure proof *)
+lemma fpbg_fpbs_trans (G) (L) (T):
+      ∀G1,L1,T1. ❪G1,L1,T1❫ > ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+#G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
+elim (fpbg_inv_gen … H1) -H1
+/3 width=13 by fpbg_intro, fpbs_trans/
 qed-.