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

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  14
  15 include "basic_2/notation/relations/predtysn_4.ma".
  16 include "basic_2/relocation/lex.ma".
  17 include "basic_2/rt_transition/cpx.ma".
  18
  19 (* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENVIRONMENTS ******************)
  20
  21 definition lpx: sh → genv → relation lenv ≝
  22                 λh,G. lex (cpx h G).
  23
  24 interpretation
  25    "uncounted parallel rt-transition (local environment)"
  26    'PRedTySn h G L1 L2 = (lpx h G L1 L2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 (*
  31 lemma lpx_pair: ∀h,g,I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 → ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 →
  32                 ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2.
  33 /2 width=1 by lpx_sn_pair/ qed.
  34 *)
  35
  36 lemma lpx_refl: ∀h,G. reflexive … (lpx h G).
  37 /2 width=1 by lex_refl/ qed.
  38
  39 (* Basic inversion lemmas ***************************************************)
  40
  41 (* Basic_2A1: was: lpx_inv_atom1 *)
  42 lemma lpx_inv_atom_sn: ∀h,G,L2. ⦃G, ⋆⦄ ⊢ ⬈[h] L2 → L2 = ⋆.
  43 /2 width=2 by lex_inv_atom_sn/ qed-.
  44
  45 (* Basic_2A1: was: lpx_inv_pair1 *)
  46 lemma lpx_inv_pair_sn: ∀h,I,G,L2,K1,V1. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] L2 →
  47                        ∃∃K2,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
  48                                 L2 = K2.ⓑ{I}V2.
  49 /2 width=1 by lex_inv_pair_sn/ qed-.
  50
  51 (* Basic_2A1: was: lpx_inv_atom2 *)
  52 lemma lpx_inv_atom_dx: ∀h,G,L1.  ⦃G, L1⦄ ⊢ ⬈[h] ⋆ → L1 = ⋆.
  53 /2 width=2 by lex_inv_atom_dx/ qed-.
  54
  55 (* Basic_2A1: was: lpx_inv_pair2 *)
  56 lemma lpx_inv_pair2_dx: ∀h,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2 →
  57                         ∃∃K1,V1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
  58                                  L1 = K1.ⓑ{I}V1.
  59 /2 width=1 by lex_inv_pair_dx/ qed-.
  60
  61 (* Advanced inversion lemmas ************************************************)
  62
  63 lemma lpx_inv_pair: ∀h,I1,I2,G,L1,L2,V1,V2.  ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ⬈[h] L2.ⓑ{I2}V2 →
  64                     ∧∧ ⦃G, L1⦄ ⊢ ⬈[h] L2 & ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 & I1 = I2.
  65 /2 width=1 by lex_inv_pair/ qed-.