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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/static/lfxs_fqup.ma".
16 include "basic_2/rt_transition/lfpx.ma".
18 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
20 (* Advanced properties ******************************************************)
22 lemma lfpx_refl: ∀h,G,T. reflexive … (lfpx h G T).
23 /2 width=1 by lfxs_refl/ qed.
25 lemma lfpx_pair_refl: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
26 ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ⬈[h, T] L.ⓑ{I}V2.
27 /2 width=1 by lfxs_pair_refl/ qed.
29 (* Advanced inversion lemmas ************************************************)
31 lemma lfpx_inv_bind_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2 →
32 ∧∧ ⦃G, L1⦄ ⊢ ⬈[h, V] L2 & ⦃G, L1.ⓧ⦄ ⊢ ⬈[h, T] L2.ⓧ.
33 /2 width=3 by lfxs_inv_bind_void/ qed-.
35 (* Advanced forward lemmas **************************************************)
37 lemma lfpx_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T.
38 ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L2 → ⦃G, L1.ⓧ⦄ ⊢ ⬈[h, T] L2.ⓧ.
39 /2 width=4 by lfxs_fwd_bind_dx_void/ qed-.