(* Properties with contextual transitive closure ****************************)
lemma lprs_CTC (h) (G):
- ∀L1,L2. L1⪤[CTC … (λL. cpm h G L 0)] L2 → ❪G,L1❫⊢ ➡*[h] L2.
+ ∀L1,L2. L1⪤[CTC … (λL. cpm h G L 0)] L2 → ❪G,L1❫⊢ ➡*[h,0] L2.
/3 width=3 by cprs_CTC, lex_co/ qed.
(* Inversion lemmas with contextual transitive closure **********************)
lemma lprs_inv_CTC (h) (G):
- ∀L1,L2. ❪G,L1❫⊢ ➡*[h] L2 → L1⪤[CTC … (λL. cpm h G L 0)] L2.
+ ∀L1,L2. ❪G,L1❫⊢ ➡*[h,0] L2 → L1⪤[CTC … (λL. cpm h G L 0)] L2.
/3 width=3 by cprs_inv_CTC, lex_co/ qed-.