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

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  14
  15 include "basic_2/notation/relations/predsubtyproper_6.ma".
  16 include "static_2/static/feqx.ma".
  17 include "basic_2/rt_transition/fpb.ma".
  18
  19 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  20
  21 (* Basic_2A1: uses: fpb *)
  22 definition fpbc (G1) (L1) (T1) (G2) (L2) (T2): Prop ≝
  23            ∧∧ ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩
  24             & (❨G1,L1,T1❩ ≅ ❨G2,L2,T2❩ → ⊥).
  25
  26 interpretation
  27   "proper parallel rst-transition (closure)"
  28   'PRedSubTyProper G1 L1 T1 G2 L2 T2 = (fpbc G1 L1 T1 G2 L2 T2).
  29
  30 (* Basic properties *********************************************************)
  31
  32 (* Basic_2A1: fpbq_inv_fpb_alt *)
  33 lemma fpbc_intro (G1) (L1) (T1) (G2) (L2) (T2):
  34       ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩ → (❨G1,L1,T1❩ ≅ ❨G2,L2,T2❩ → ⊥) →
  35       ❨G1,L1,T1❩ ≻ ❨G2,L2,T2❩.
  36 /3 width=1 by conj/ qed.
  37
  38 lemma rpx_fpbc (G) (T):
  39       ∀L1,L2. ❨G,L1❩ ⊢ ⬈[T] L2 → (L1 ≅[T] L2 → ⊥) → ❨G,L1,T❩ ≻ ❨G,L2,T❩.
  40 /4 width=4 by fpbc_intro, rpx_fpb, feqg_fwd_reqg_sn/ qed.
  41
  42 (* Basic inversion lemmas ***************************************************)
  43
  44 (* Basic_2A1: uses: fpb_fpbq_alt *)
  45 lemma fpbc_inv_gen (S):
  46       ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ≻ ❨G2,L2,T2❩ →
  47       ∧∧ ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩ & (❨G1,L1,T1❩ ≛[S] ❨G2,L2,T2❩ → ⊥).
  48 #S #G1 #G2 #L1 #L2 #T1 #T2 *
  49 /4 width=2 by feqg_feqx, conj/
  50 qed-.
  51
  52 (* Basic forward lemmas *****************************************************)
  53
  54 (* Basic_2A1: uses: fpb_fpbq *)
  55 lemma fpbc_fwd_fpb:
  56       ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ≻ ❨G2,L2,T2❩ →
  57       ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩.
  58 #G1 #G2 #L1 #L2 #T1 #T2 * //
  59 qed-.