matita/matita/contribs/lambdadelta/basic_2/relocation/fsupq_alt.ma

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  14
  15 include "basic_2/notation/relations/suptermoptalt_4.ma".
  16 include "basic_2/relocation/fsupq.ma".
  17
  18 (* OPTIONAL SUPCLOSURE ******************************************************)
  19
  20 (* alternative definition of fsupq *)
  21 definition fsupqa: bi_relation lenv term ≝ bi_RC … fsup.
  22
  23 interpretation
  24    "optional structural successor (closure) alternative"
  25    'SupTermOptAlt L1 T1 L2 T2 = (fsupqa L1 T1 L2 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma fsupqa_refl: bi_reflexive … fsupqa.
  30 // qed.
  31
  32 lemma fsupqa_ldrop: ∀K1,K2,T1,T2. ⦃K1, T1⦄ ⊃⊃⸮ ⦃K2, T2⦄ →
  33                     ∀L1,d,e. ⇩[d, e] L1 ≡ K1 →
  34                     ∀U1. ⇧[d, e] T1 ≡ U1 → ⦃L1, U1⦄ ⊃⊃⸮ ⦃K2, T2⦄.
  35 #K1 #K2 #T1 #T2 * [ /3 width=7/ ] * #H1 #H2 destruct
  36 #L1 #d #e #HLK #U1 #HTU elim (eq_or_gt e) [2: /3 width=5/ ] #H destruct
  37 >(ldrop_inv_O2 … HLK) -L1 >(lift_inv_O2 … HTU) -T2 -d //
  38 qed.
  39
  40 (* Main properties **********************************************************)
  41
  42 theorem fsupq_fsupqa: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃⊃⸮ ⦃L2, T2⦄.
  43 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 // /2 width=1/ /2 width=7/
  44 qed.
  45
  46 (* Main inversion properties ************************************************)
  47
  48 theorem fsupqa_inv_fsupq: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃⊃⸮ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄.
  49 #L1 #L2 #T1 #T2 #H elim H -H /2 width=1/
  50 * #H1 #H2 destruct //
  51 qed-.