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 c052a3a3c09a0be9e13606f4b38b80260391d643..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
@@ -12,59 +12,52 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/xoa/ex_2_3.ma".
+include "ground/xoa/ex_3_6.ma".
 include "basic_2/notation/relations/predsubtystarproper_6.ma".
-include "basic_2/rt_transition/fpb.ma".
+include "basic_2/rt_transition/fpbc.ma".
 include "basic_2/rt_computation/fpbs.ma".
 
 (* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
 definition fpbg: tri_relation genv lenv term ≝
            λG1,L1,T1,G2,L2,T2.
-           ∃∃G,L,T. ❪G1,L1,T1❫ ≻ ❪G,L,T❫ & ❪G,L,T❫ ≥ ❪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 G1 L1 T1 G2 L2 T2 = (fpbg 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 inversion lemmas ***************************************************)
+
+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-.
 
 (* Basic properties *********************************************************)
 
-lemma fpb_fpbg:
-      ∀G1,G2,L1,L2,T1,T2.
-      ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
-/2 width=5 by ex2_3_intro/ qed.
+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.
 
-lemma fpbg_fpbq_trans:
+(* 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 *
-/3 width=9 by fpbs_strap1, ex2_3_intro/
+#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-.
 
-lemma fpbg_fqu_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❫ ≽ ❪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
-/4 width=5 by fpbg_fpbq_trans, fpbq_fquq, fqu_fquq/
-qed-.
-
-(* Note: this is used in the closure proof *)
-lemma fpbg_fpbs_trans: 
-      ∀G,G2,L,L2,T,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ →
-      ∀G1,L1,T1. ❪G1,L1,T1❫ > ❪G,L,T❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
-#G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpbq_trans/
+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:
-      ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ > ❪G,L,T❫ →
-      ∀G2,L2,T2. ❪G,L,T❫ ≅ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪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❫ > ❪G,L,T2❫.
-/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.