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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "static_2/notation/relations/suptermopt_6.ma".
16 include "static_2/notation/relations/suptermopt_7.ma".
17 include "static_2/s_transition/fqu.ma".
19 (* OPTIONAL SUPCLOSURE ******************************************************)
21 (* Basic_2A1: was: fquqa *)
22 (* Basic_2A1: includes: fquq_inv_gen *)
23 definition fquq: bool → tri_relation genv lenv term ≝
27 "extended optional structural successor (closure)"
28 'SupTermOpt b G1 L1 T1 G2 L2 T2 = (fquq b G1 L1 T1 G2 L2 T2).
31 "optional structural successor (closure)"
32 'SupTermOpt G1 L1 T1 G2 L2 T2 = (fquq true G1 L1 T1 G2 L2 T2).
34 (* Basic properties *********************************************************)
36 (* Basic_2A1: includes: fquqa_refl *)
37 lemma fquq_refl: ∀b. tri_reflexive … (fquq b).
40 lemma fqu_fquq: ∀b,G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂[b] ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ⬂⸮[b] ❨G2,L2,T2❩.
41 /2 width=1 by or_introl/ qed.
43 (* Basic_2A1: removed theorems 8:
44 fquq_lref_O fquq_pair_sn fquq_bind_dx fquq_flat_dx fquq_drop
45 fquqa_drop fquq_fquqa fquqa_inv_fquq