milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
index 8d940a856aa7f28a1a3161d81a23367dab006352..5c6176697fc77bf14924e4d8cf6c57a01d70f59d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
@@ -12,56 +12,52 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/xoa/ex_2_3.ma".
-include "basic_2/notation/relations/predsubtystarproper_7.ma".
-include "basic_2/rt_transition/fpb.ma".
+include "ground/xoa/ex_3_6.ma".
+include "basic_2/notation/relations/predsubtystarproper_6.ma".
+include "basic_2/rt_transition/fpbc.ma".
 include "basic_2/rt_computation/fpbs.ma".
 
 (* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
-definition fpbg: ∀h. tri_relation genv lenv term ≝
-           λh,G1,L1,T1,G2,L2,T2.
-           ∃∃G,L,T. ❪G1,L1,T1❫ ≻[h] ❪G,L,T❫ & ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫.
+definition fpbg: tri_relation genv lenv term ≝
+           λG1,L1,T1,G2,L2,T2.
+           ∃∃G3,L3,T3,G4,L4,T4. ❪G1,L1,T1❫ ≥ ❪G3,L3,T3❫ & ❪G3,L3,T3❫ ≻ ❪G4,L4,T4❫ & ❪G4,L4,T4❫ ≥ ❪G2,L2,T2❫.
 
-interpretation "proper parallel rst-computation (closure)"
-   'PRedSubTyStarProper h G1 L1 T1 G2 L2 T2 = (fpbg h G1 L1 T1 G2 L2 T2).
+interpretation
+  "proper parallel rst-computation (closure)"
+  'PRedSubTyStarProper G1 L1 T1 G2 L2 T2 = (fpbg G1 L1 T1 G2 L2 T2).
 
-(* Basic properties *********************************************************)
+(* Basic inversion lemmas ***************************************************)
 
-lemma fpb_fpbg: ∀h,G1,G2,L1,L2,T1,T2.
-      ❪G1,L1,T1❫ ≻[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
-/2 width=5 by ex2_3_intro/ qed.
+lemma fpbg_inv_gen (G1) (G2) (L1) (L2) (T1) (T2):
+      ❪G1,L1,T1❫ > ❪G2,L2,T2❫ →
+      ∃∃G3,L3,T3,G4,L4,T4. ❪G1,L1,T1❫ ≥ ❪G3,L3,T3❫ & ❪G3,L3,T3❫ ≻ ❪G4,L4,T4❫ & ❪G4,L4,T4❫ ≥ ❪G2,L2,T2❫.
+// qed-.
 
-lemma fpbg_fpbq_trans: ∀h,G1,G,G2,L1,L,L2,T1,T,T2.
-      ❪G1,L1,T1❫ >[h] ❪G,L,T❫ → ❪G,L,T❫ ≽[h] ❪G2,L2,T2❫ →
-      ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
-#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
-/3 width=9 by fpbs_strap1, ex2_3_intro/
-qed-.
+(* Basic properties *********************************************************)
 
-lemma fpbg_fqu_trans (h): ∀G1,G,G2,L1,L,L2,T1,T,T2.
-      ❪G1,L1,T1❫ >[h] ❪G,L,T❫ → ❪G,L,T❫ ⬂ ❪G2,L2,T2❫ →
-      ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
-#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
-/4 width=5 by fpbg_fpbq_trans, fpbq_fquq, fqu_fquq/
+lemma fpbg_intro (G3) (G4) (L3) (L4) (T3) (T4):
+      ∀G1,L1,T1,G2,L2,T2.
+      ❪G1,L1,T1❫ ≥ ❪G3,L3,T3❫ → ❪G3,L3,T3❫ ≻ ❪G4,L4,T4❫ →
+      ❪G4,L4,T4❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+/2 width=9 by ex3_6_intro/ qed.
+
+(* Basic_2A1: was: fpbg_fpbq_trans *)
+lemma fpbg_fpb_trans:
+      ∀G1,G,G2,L1,L,L2,T1,T,T2.
+      ❪G1,L1,T1❫ > ❪G,L,T❫ → ❪G,L,T❫ ≽ ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+#G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
+elim (fpbg_inv_gen … H1) -H1
+/3 width=13 by fpbs_strap1, fpbg_intro/
 qed-.
 
-(* Note: this is used in the closure proof *)
-lemma fpbg_fpbs_trans: ∀h,G,G2,L,L2,T,T2.
-      ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫ →
-      ∀G1,L1,T1. ❪G1,L1,T1❫ >[h] ❪G,L,T❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
-#h #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
+(* Basic_2A1: was: fpbq_fpbg_trans *)
+lemma fpb_fpbg_trans:
+      ∀G1,G,G2,L1,L,L2,T1,T,T2.
+      ❪G1,L1,T1❫ ≽ ❪G,L,T❫ → ❪G,L,T❫ > ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+#G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
+elim (fpbg_inv_gen … H2) -H2
+/3 width=13 by fpbs_strap2, fpbg_intro/
 qed-.
-
-(* Basic_2A1: uses: fpbg_fleq_trans *)
-lemma fpbg_feqx_trans: ∀h,G1,G,L1,L,T1,T.
-      ❪G1,L1,T1❫ >[h] ❪G,L,T❫ →
-      ∀G2,L2,T2. ❪G,L,T❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
-/3 width=5 by fpbg_fpbq_trans, fpbq_feqx/ qed-.
-
-(* Properties with t-bound rt-transition for terms **************************)
-
-lemma cpm_tneqx_cpm_fpbg (h) (G) (L):
-      ∀n1,T1,T. ❪G,L❫ ⊢ T1 ➡[h,n1] T → (T1 ≛ T → ⊥) →
-      ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 → ❪G,L,T1❫ >[h] ❪G,L,T2❫.
-/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.