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14
15 notation "hvbox( ⦃ term 46 L1 ⦄ ➡ break ⦃ term 46 L2 ⦄ )"
16    non associative with precedence 45
17    for @{ 'FocalizedPRed $L1 $L2 }.
18
19 include "basic_2/unfold/ltpss_sn.ma".
20 include "basic_2/reducibility/ltpr.ma".
21
22 (* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
23
24 definition lfpr: relation lenv ≝
25    λL1,L2. ∃∃L. L1 ➡ L & L ⊢ ▶* [0, |L|] L2
26 .
27
28 interpretation
29   "focalized parallel reduction (environment)"
30   'FocalizedPRed L1 L2 = (lfpr L1 L2).
31
32 (* Basic properties *********************************************************)
33
34 (* Note: lemma 250 *)
35 lemma lfpr_refl: ∀L. ⦃L⦄ ➡ ⦃L⦄.
36 /2 width=3/ qed.
37
38 lemma ltpss_sn_lfpr: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 → ⦃L1⦄ ➡ ⦃L2⦄.
39 /3 width=5/ qed.
40
41 lemma ltpr_lfpr: ∀L1,L2. L1 ➡ L2 → ⦃L1⦄ ➡ ⦃L2⦄.
42 /3 width=3/ qed.
43
44 (* Basic inversion lemmas ***************************************************)
45
46 lemma lfpr_inv_atom1: ∀L2. ⦃⋆⦄ ➡ ⦃L2⦄ → L2 = ⋆.
47 #L2 * #L #HL >(ltpr_inv_atom1 … HL) -HL #HL2 >(ltpss_sn_inv_atom1 … HL2) -HL2 //
48 qed-.