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

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  14
  15 include "basic_2/notation/relations/predsubty_6.ma".
  16 include "static_2/s_transition/fquq.ma".
  17 include "basic_2/rt_transition/rpx.ma".
  18
  19 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
  20
  21 (* Basic_2A1: uses: fpbq *)
  22 definition fpb (G1) (L1) (T1) (G2) (L2) (T2): Prop ≝
  23            ∃∃L,T. ❨G1,L1,T1❩ ⬂⸮ ❨G2,L,T❩ & ❨G2,L❩ ⊢ T ⬈ T2 & ❨G2,L❩ ⊢ ⬈[T] L2.
  24
  25 interpretation
  26   "parallel rst-transition (closure)"
  27   'PRedSubTy G1 L1 T1 G2 L2 T2 = (fpb G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma fpb_intro (G1) (L1) (T1) (G2) (L2) (T2):
  32       ∀L,T. ❨G1,L1,T1❩ ⬂⸮ ❨G2,L,T❩ → ❨G2,L❩ ⊢ T ⬈ T2 →
  33       ❨G2,L❩ ⊢ ⬈[T] L2 → ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩.
  34 /2 width=5 by ex3_2_intro/ qed.
  35
  36 lemma rpx_fpb (G) (T):
  37       ∀L1,L2. ❨G,L1❩ ⊢ ⬈[T] L2 → ❨G,L1,T❩ ≽ ❨G,L2,T❩.
  38 /2 width=5 by fpb_intro/ qed.
  39
  40 (* Basic inversion lemmas ***************************************************)
  41
  42 lemma fpb_inv_gen (G1) (L1) (T1) (G2) (L2) (T2):
  43       ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩ →
  44       ∃∃L,T. ❨G1,L1,T1❩ ⬂⸮ ❨G2,L,T❩ & ❨G2,L❩ ⊢ T ⬈ T2 & ❨G2,L❩ ⊢ ⬈[T] L2.
  45 // qed-.
  46
  47 (* Basic_2A1: removed theorems 2:
  48               fpbq_fpbqa fpbqa_inv_fpbq
  49 *)