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15 include "basic_2/unfold/ltpss_sn.ma".
16 include "basic_2/reducibility/ltpr.ma".
18 (* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
20 definition lfpr: relation lenv ≝
21 λL1,L2. ∃∃L. L1 ➡ L & L ⊢ ▶* [0, |L|] L2
25 "focalized parallel reduction (environment)"
26 'FocalizedPRed L1 L2 = (lfpr L1 L2).
28 (* Basic properties *********************************************************)
31 lemma lfpr_refl: ∀L. ⦃L⦄ ➡ ⦃L⦄.
34 lemma ltpss_sn_lfpr: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 → ⦃L1⦄ ➡ ⦃L2⦄.
37 (* Basic inversion lemmas ***************************************************)
39 lemma lfpr_inv_atom1: ∀L2. ⦃⋆⦄ ➡ ⦃L2⦄ → L2 = ⋆.
40 #L2 * #L #HL >(ltpr_inv_atom1 … HL) -HL #HL2 >(ltpss_sn_inv_atom1 … HL2) -HL2 //