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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 "basic_2/rt_transition/rpx_fqup.ma".
16 include "basic_2/rt_transition/fpb.ma".
18 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
20 (* Advanced properties ******************************************************)
22 (* Basic_2A1: was: fpbq_refl *)
23 lemma fpb_refl: tri_reflexive … fpb.
24 /2 width=5 by fpb_intro/ qed.
26 (* Basic_2A1: uses: fpbq_cpx *)
27 lemma cpx_fpb (G) (L):
28 ∀T1,T2. ❪G,L❫ ⊢ T1 ⬈ T2 → ❪G,L,T1❫ ≽ ❪G,L,T2❫.
29 /2 width=5 by fpb_intro/ qed.
31 (* Basic_2A1: uses: fpbq_fquq *)
32 lemma fquq_fpb (G1) (G2) (L1) (L2) (T1) (T2):
33 ❪G1,L1,T1❫ ⬂⸮ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
34 /2 width=5 by fpb_intro/ qed.
36 lemma fqu_fpb (G1) (G2) (L1) (L2) (T1) (T2):
37 ❪G1,L1,T1❫ ⬂ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
38 /3 width=5 by fquq_fpb, fqu_fquq/ qed.