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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/relocation/fsupq.ma".
17 (* OPTIONAL SUPCLOSURE ******************************************************)
19 (* alternative definition of fsupq *)
20 definition fsupqa: bi_relation lenv term ≝ bi_RC … fsup.
23 "optional structural successor (closure) alternative"
24 'SupTermOptAlt L1 T1 L2 T2 = (fsupqa L1 T1 L2 T2).
26 (* Basic properties *********************************************************)
28 lemma fsupqa_refl: bi_reflexive … fsupqa.
31 lemma fsupqa_ldrop: ∀K1,K2,T1,T2. ⦃K1, T1⦄ ⊃⊃⸮ ⦃K2, T2⦄ →
32 ∀L1,d,e. ⇩[d, e] L1 ≡ K1 →
33 ∀U1. ⇧[d, e] T1 ≡ U1 → ⦃L1, U1⦄ ⊃⊃⸮ ⦃K2, T2⦄.
34 #K1 #K2 #T1 #T2 * [ /3 width=7/ ] * #H1 #H2 destruct
35 #L1 #d #e #HLK #U1 #HTU elim (eq_or_gt e) [2: /3 width=5/ ] #H destruct
36 >(ldrop_inv_O2 … HLK) -L1 >(lift_inv_O2 … HTU) -T2 -d //
39 (* Main properties **********************************************************)
41 theorem fsupq_fsupqa: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃⊃⸮ ⦃L2, T2⦄.
42 #L1 #L2 #T1 #T2 #H elim H -L1 -L2 -T1 -T2 // /2 width=1/ /2 width=7/
45 (* Main inversion properties ************************************************)
47 theorem fsupqa_inv_fsupq: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃⊃⸮ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄.
48 #L1 #L2 #T1 #T2 #H elim H -H /2 width=1/