matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma

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  14
  15 include "basic_2/notation/relations/predsubtyproper_8.ma".
  16 include "static_2/s_transition/fqu.ma".
  17 include "static_2/static/rdeq.ma".
  18 include "basic_2/rt_transition/lpr_lpx.ma".
  19
  20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  21
  22 inductive fpb (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝
  23 | fpb_fqu: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h o G1 L1 T1 G2 L2 T2
  24 | fpb_cpx: ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2
  25 | fpb_lpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T1] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1
  26 .
  27
  28 interpretation
  29    "proper parallel rst-transition (closure)"
  30    'PRedSubTyProper h o G1 L1 T1 G2 L2 T2 = (fpb h o G1 L1 T1 G2 L2 T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 (* Basic_2A1: includes: cpr_fpb *)
  35 lemma cpm_fpb (n) (h) (o) (G) (L): ∀T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → (T1 ≛[h, o] T2 → ⊥) →
  36                                    ⦃G, L, T1⦄ ≻[h, o] ⦃G, L, T2⦄.
  37 /3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
  38
  39 lemma lpr_fpb (h) (o) (G) (T): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) →
  40                            ⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄.
  41 /3 width=1 by fpb_lpx, lpr_fwd_lpx/ qed.