1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "static_2/static/rex_rex.ma".
16 include "basic_2/rt_transition/rpx.ma".
18 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
20 (* Main properties **********************************************************)
23 ∀L1,L2,V1. ❨G,L1❩ ⊢ ⬈[V1] L2 →
24 ∀I,V2,T. ❨G,L1.ⓑ[I]V1❩ ⊢ ⬈[T] L2.ⓑ[I]V2 →
25 ∀p. ❨G,L1❩ ⊢ ⬈[ⓑ[p,I]V1.T] L2.
26 /2 width=2 by rex_bind/ qed.
29 ∀L1,L2,V. ❨G,L1❩ ⊢ ⬈[V] L2 →
30 ∀I,T. ❨G,L1❩ ⊢ ⬈[T] L2 → ❨G,L1❩ ⊢ ⬈[ⓕ[I]V.T] L2.
31 /2 width=1 by rex_flat/ qed.
33 theorem rpx_bind_void (G):
34 ∀L1,L2,V. ❨G,L1❩ ⊢ ⬈[V] L2 →
35 ∀T. ❨G,L1.ⓧ❩ ⊢ ⬈[T] L2.ⓧ →
36 ∀p,I. ❨G,L1❩ ⊢ ⬈[ⓑ[p,I]V.T] L2.
37 /2 width=1 by rex_bind_void/ qed.