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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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11 (* v GNU General Public License Version 2 *)
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15 include "static_2/static/rex_fqup.ma".
16 include "basic_2/rt_transition/rpx.ma".
18 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
20 (* Advanced properties ******************************************************)
23 ∀T. reflexive … (rpx G T).
24 /2 width=1 by rex_refl/ qed.
26 lemma rpx_pair_refl (G):
27 ∀L,V1,V2. ❪G,L❫ ⊢ V1 ⬈ V2 →
28 ∀I,T. ❪G,L.ⓑ[I]V1❫ ⊢ ⬈[T] L.ⓑ[I]V2.
29 /2 width=1 by rex_pair_refl/ qed.
31 (* Advanced inversion lemmas ************************************************)
33 lemma rpx_inv_bind_void (G):
34 ∀p,I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2 →
35 ∧∧ ❪G,L1❫ ⊢ ⬈[V] L2 & ❪G,L1.ⓧ❫ ⊢ ⬈[T] L2.ⓧ.
36 /2 width=3 by rex_inv_bind_void/ qed-.
38 (* Advanced forward lemmas **************************************************)
40 lemma rpx_fwd_bind_dx_void (G):
41 ∀p,I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2 → ❪G,L1.ⓧ❫ ⊢ ⬈[T] L2.ⓧ.
42 /2 width=4 by rex_fwd_bind_dx_void/ qed-.