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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/static/rex_fqup.ma".
16 include "basic_2/rt_transition/rpx.ma".
18 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
20 (* Advanced properties ******************************************************)
22 lemma rpx_refl: ∀h,G,T. reflexive … (rpx h G T).
23 /2 width=1 by rex_refl/ qed.
25 lemma rpx_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 rex_pair_refl/ qed.
29 (* Advanced inversion lemmas ************************************************)
31 lemma rpx_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 rex_inv_bind_void/ qed-.
35 (* Advanced forward lemmas **************************************************)
37 lemma rpx_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 rex_fwd_bind_dx_void/ qed-.