include "basic_2/notation/relations/lazypredsnstar_7.ma".
include "basic_2/reduction/llpx.ma".
-include "basic_2/computation/llprs.ma".
(* LAZY SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS **************)
(* Basic properties *********************************************************)
-lemma llprs_llpxs: ∀h,g,G,L1,L2,T,d. ⦃G, L1⦄ ⊢ ➡*[T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g, T, d] L2.
-normalize /3 width=3 by llpr_llpx, monotonic_TC/ qed.
-
lemma llpx_llpxs: ∀h,g,G,L1,L2,T,d. ⦃G, L1⦄ ⊢ ➡[h, g, T, d] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g, T, d] L2.
normalize /2 width=1 by inj/ qed.