matita/matita/contribs/lambdadelta/basic_2/dynamic/ysc.ma

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  14
  15 include "basic_2/notation/relations/btpredproper_6.ma".
  16 include "basic_2/dynamic/ypr.ma".
  17
  18 (* "BIG TREE" PROPER PARALLEL REDUCTION FOR CLOSURES ************************)
  19
  20 inductive ysc (h) (g) (L1) (T1): relation2 lenv term ≝
  21 | ysc_fsup  : ∀L2,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ysc h g L1 T1 L2 T2
  22 | ysc_cpr   : ∀T2. L1 ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → ysc h g L1 T1 L1 T2
  23 | ysc_ssta  : ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[h, g] ⦃l+1, T2⦄ → ysc h g L1 T1 L1 T2
  24 | ysc_lsubsv: ∀L2. h ⊢ L2 ¡⊑[h, g] L1 → (L1 = L2 → ⊥) → ysc h g L1 T1 L2 T1
  25 .
  26
  27 interpretation
  28    "'big tree' proper parallel reduction (closure)"
  29    'BTPRedProper h g L1 T1 L2 T2 = (ysc h g L1 T1 L2 T2).
  30
  31 (* Basic properties *********************************************************)
  32
  33 lemma ysc_ypr: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≻[h, g] ⦃L2, T2⦄ →
  34                h ⊢ ⦃L1, T1⦄ ≽[h, g] ⦃L2, T2⦄.
  35 #h #g #L1 #L2 #T1 #T2 * -L2 -T2 /2 width=1/ /2 width=2/
  36 qed.
  37
  38 (* Inversion lemmas on "big tree" parallel reduction for closures ***********)
  39
  40 lemma ypr_inv_ysc: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≽[h, g] ⦃L2, T2⦄ →
  41                    h ⊢ ⦃L1, T1⦄ ≻[h, g] ⦃L2, T2⦄ ∨ (L1 ⊢ ➡ L2 ∧ T1 = T2).
  42 #h #g #L1 #L2 #T1 #T2 * -L2 -T2 /3 width=1/ /3 width=2/
  43 [ #T2 #HT12 elim (term_eq_dec T1 T2) #H destruct /3 width=1/ /4 width=1/
  44 | #L2 #HL21 elim (lenv_eq_dec L1 L2) #H destruct /3 width=1/ /4 width=1/
  45 ]
  46 qed-.