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14
15 include "basic_2/equivalence/cpcs_cpcs.ma".
16 include "basic_2/dynamic/lsubn.ma".
17
18 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
19
20 (* Properties on context-sensitive parallel equivalence for terms ***********)
21
22 (* Basic_1: was: csubt_pr2 *)
23 lemma cpr_lsubn_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 →
24                        ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡ T2.
25 /3 width=4 by lsubn_fwd_lsubs2, cpr_lsubs_trans/ qed.
26
27 lemma cprs_lsubn_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 →
28                         ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
29 /3 width=4 by lsubn_fwd_lsubs2, cprs_lsubs_trans/ qed.
30
31 (* Basic_1: was: csubt_pc3 *)
32 lemma cpcs_lsubn_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 →
33                         ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
34 /3 width=4 by lsubn_fwd_lsubs2, cpcs_lsubs_trans/ qed.