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 *)
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15 include "static_2/static/rex_rex.ma".
16 include "basic_2/rt_transition/rpx.ma".
18 (* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
20 (* Main properties **********************************************************)
22 theorem rpx_bind: ∀h,G,L1,L2,V1. ❪G,L1❫ ⊢ ⬈[h,V1] L2 →
23 ∀I,V2,T. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[h,T] L2.ⓑ[I]V2 →
24 ∀p. ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V1.T] L2.
25 /2 width=2 by rex_bind/ qed.
27 theorem rpx_flat: ∀h,G,L1,L2,V. ❪G,L1❫ ⊢ ⬈[h,V] L2 →
28 ∀I,T. ❪G,L1❫ ⊢ ⬈[h,T] L2 → ❪G,L1❫ ⊢ ⬈[h,ⓕ[I]V.T] L2.
29 /2 width=1 by rex_flat/ qed.
31 theorem rpx_bind_void: ∀h,G,L1,L2,V. ❪G,L1❫ ⊢ ⬈[h,V] L2 →
32 ∀T. ❪G,L1.ⓧ❫ ⊢ ⬈[h,T] L2.ⓧ →
33 ∀p,I. ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V.T] L2.
34 /2 width=1 by rex_bind_void/ qed.