include "static_2/static/rex_rex.ma".
include "basic_2/rt_transition/rpx.ma".
-(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+(* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
(* Main properties **********************************************************)
-theorem rpx_bind: ∀h,G,L1,L2,V1. ❪G,L1❫ ⊢ ⬈[h,V1] L2 →
- ∀I,V2,T. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[h,T] L2.ⓑ[I]V2 →
- ∀p. ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V1.T] L2.
+theorem rpx_bind (G):
+ ∀L1,L2,V1. ❪G,L1❫ ⊢ ⬈[V1] L2 →
+ ∀I,V2,T. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[T] L2.ⓑ[I]V2 →
+ ∀p. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V1.T] L2.
/2 width=2 by rex_bind/ qed.
-theorem rpx_flat: ∀h,G,L1,L2,V. ❪G,L1❫ ⊢ ⬈[h,V] L2 →
- ∀I,T. ❪G,L1❫ ⊢ ⬈[h,T] L2 → ❪G,L1❫ ⊢ ⬈[h,ⓕ[I]V.T] L2.
+theorem rpx_flat (G):
+ ∀L1,L2,V. ❪G,L1❫ ⊢ ⬈[V] L2 →
+ ∀I,T. ❪G,L1❫ ⊢ ⬈[T] L2 → ❪G,L1❫ ⊢ ⬈[ⓕ[I]V.T] L2.
/2 width=1 by rex_flat/ qed.
-theorem rpx_bind_void: ∀h,G,L1,L2,V. ❪G,L1❫ ⊢ ⬈[h,V] L2 →
- ∀T. ❪G,L1.ⓧ❫ ⊢ ⬈[h,T] L2.ⓧ →
- ∀p,I. ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V.T] L2.
+theorem rpx_bind_void (G):
+ ∀L1,L2,V. ❪G,L1❫ ⊢ ⬈[V] L2 →
+ ∀T. ❪G,L1.ⓧ❫ ⊢ ⬈[T] L2.ⓧ →
+ ∀p,I. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2.
/2 width=1 by rex_bind_void/ qed.