include "static_2/static/rex_fqup.ma".
include "basic_2/rt_transition/rpx.ma".
-(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+(* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
(* Advanced properties ******************************************************)
-lemma rpx_refl: ∀h,G,T. reflexive … (rpx h G T).
+lemma rpx_refl (G):
+ ∀T. reflexive … (rpx G T).
/2 width=1 by rex_refl/ qed.
-lemma rpx_pair_refl: ∀h,G,L,V1,V2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 →
- ∀I,T. ⦃G,L.ⓑ{I}V1⦄ ⊢ ⬈[h,T] L.ⓑ{I}V2.
+lemma rpx_pair_refl (G):
+ ∀L,V1,V2. ❪G,L❫ ⊢ V1 ⬈ V2 →
+ ∀I,T. ❪G,L.ⓑ[I]V1❫ ⊢ ⬈[T] L.ⓑ[I]V2.
/2 width=1 by rex_pair_refl/ qed.
(* Advanced inversion lemmas ************************************************)
-lemma rpx_inv_bind_void: ∀h,p,I,G,L1,L2,V,T. ⦃G,L1⦄ ⊢ ⬈[h,ⓑ{p,I}V.T] L2 →
- ∧∧ ⦃G,L1⦄ ⊢ ⬈[h,V] L2 & ⦃G,L1.ⓧ⦄ ⊢ ⬈[h,T] L2.ⓧ.
+lemma rpx_inv_bind_void (G):
+ ∀p,I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2 →
+ ∧∧ ❪G,L1❫ ⊢ ⬈[V] L2 & ❪G,L1.ⓧ❫ ⊢ ⬈[T] L2.ⓧ.
/2 width=3 by rex_inv_bind_void/ qed-.
(* Advanced forward lemmas **************************************************)
-lemma rpx_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T.
- ⦃G,L1⦄ ⊢ ⬈[h,ⓑ{p,I}V.T] L2 → ⦃G,L1.ⓧ⦄ ⊢ ⬈[h,T] L2.ⓧ.
+lemma rpx_fwd_bind_dx_void (G):
+ ∀p,I,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[ⓑ[p,I]V.T] L2 → ❪G,L1.ⓧ❫ ⊢ ⬈[T] L2.ⓧ.
/2 width=4 by rex_fwd_bind_dx_void/ qed-.