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15 include "basic_2/unfold/ltpss.ma".
16 include "basic_2/reducibility/ltpr.ma".
18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *************)
20 definition lcpr: relation lenv ≝
21 λL1,L2. ∃∃L. L1 ➡ L & L ▶* [0, |L|] L2
25 "context-sensitive parallel reduction (environment)"
26 'CPRed L1 L2 = (lcpr L1 L2).
28 (* Basic properties *********************************************************)
30 lemma lcpr_refl: ∀L. L ⊢ ➡ L.
33 (* Basic inversion lemmas ***************************************************)
35 lemma lcpr_inv_atom1: ∀L2. ⋆ ⊢ ➡ L2 → L2 = ⋆.
36 #L2 * #L #HL >(ltpr_inv_atom1 … HL) -HL #HL2 >(ltpss_inv_atom1 … HL2) -HL2 //