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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/grammar/lenv_px.ma".
16 include "basic_2/reducibility/tpr.ma".
18 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
20 definition ltpr: relation lenv ≝ lpx tpr.
23 "context-free parallel reduction (environment)"
24 'PRed L1 L2 = (ltpr L1 L2).
26 (* Basic properties *********************************************************)
28 lemma ltpr_refl: reflexive … ltpr.
31 (* Basic inversion lemmas ***************************************************)
33 (* Basic_1: was: wcpr0_gen_sort *)
34 lemma ltpr_inv_atom1: ∀L2. ⋆ ➡ L2 → L2 = ⋆.
35 /2 width=2 by lpx_inv_atom1/ qed-.
37 (* Basic_1: was: wcpr0_gen_head *)
38 lemma ltpr_inv_pair1: ∀K1,I,V1,L2. K1. ⓑ{I} V1 ➡ L2 →
39 ∃∃K2,V2. K1 ➡ K2 & V1 ➡ V2 & L2 = K2. ⓑ{I} V2.
40 /2 width=1 by lpx_inv_pair1/ qed-.
42 lemma ltpr_inv_atom2: ∀L1. L1 ➡ ⋆ → L1 = ⋆.
43 /2 width=2 by lpx_inv_atom2/ qed-.
45 lemma ltpr_inv_pair2: ∀L1,K2,I,V2. L1 ➡ K2. ⓑ{I} V2 →
46 ∃∃K1,V1. K1 ➡ K2 & V1 ➡ V2 & L1 = K1. ⓑ{I} V1.
47 /2 width=1 by lpx_inv_pair2/ qed-.
49 (* Basic forward lemmas *****************************************************)
51 lemma ltpr_fwd_length: ∀L1,L2. L1 ➡ L2 → |L1| = |L2|.
52 /2 width=2 by lpx_fwd_length/ qed-.
54 (* Basic_1: removed theorems 2: wcpr0_getl wcpr0_getl_back *)