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

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  14
  15 include "basic_2/notation/relations/predsubtyproper_7.ma".
  16 include "static_2/s_transition/fqu.ma".
  17 include "static_2/static/reqx.ma".
  18 include "basic_2/rt_transition/lpr_lpx.ma".
  19
  20 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  21
  22 inductive fpb (h) (G1) (L1) (T1): relation3 genv lenv term ≝
  23 | fpb_fqu: ∀G2,L2,T2. ❪G1,L1,T1❫ ⬂ ❪G2,L2,T2❫ → fpb h G1 L1 T1 G2 L2 T2
  24 | fpb_cpx: ∀T2. ❪G1,L1❫ ⊢ T1 ⬈[h] T2 → (T1 ≛ T2 → ⊥) → fpb h G1 L1 T1 G1 L1 T2
  25 | fpb_lpx: ∀L2. ❪G1,L1❫ ⊢ ⬈[h] L2 → (L1 ≛[T1] L2 → ⊥) → fpb h G1 L1 T1 G1 L2 T1
  26 .
  27
  28 interpretation
  29    "proper parallel rst-transition (closure)"
  30    'PRedSubTyProper h G1 L1 T1 G2 L2 T2 = (fpb h G1 L1 T1 G2 L2 T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 (* Basic_2A1: includes: cpr_fpb *)
  35 lemma cpm_fpb (h) (n) (G) (L): ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[h,n] T2 → (T1 ≛ T2 → ⊥) →
  36                                    ❪G,L,T1❫ ≻[h] ❪G,L,T2❫.
  37 /3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
  38
  39 lemma lpr_fpb (h) (G) (T): ∀L1,L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → (L1 ≛[T] L2 → ⊥) →
  40                            ❪G,L1,T❫ ≻[h] ❪G,L2,T❫.
  41 /3 width=1 by fpb_lpx, lpr_fwd_lpx/ qed.