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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
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15 include "basic_2/i_static/tc_lfxs_lex.ma".
16 include "basic_2/rt_transition/cpx_lfeq.ma".
17 include "basic_2/rt_computation/cpxs_lpx.ma".
18 include "basic_2/rt_computation/lpxs.ma".
19 include "basic_2/rt_computation/lfpxs.ma".
21 (* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ******)
23 (* Properties with unbound parallel rt-computation for local environments ***)
25 lemma lfpxs_lpxs: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
26 /2 width=1 by tc_lfxs_lex/ qed.
28 lemma lfpxs_lpxs_lfeq: ∀h,G,L1,L. ⦃G, L1⦄ ⊢ ⬈*[h] L →
29 ∀L2,T. L ≡[T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
30 /2 width=3 by tc_lfxs_lex_lfeq/ qed.
32 (* Inversion lemmas with unbound parallel rt-computation for local envs *****)
34 lemma lfpxs_inv_lpxs_lfeq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 →
35 ∃∃L. ⦃G, L1⦄ ⊢ ⬈*[h] L & L ≡[T] L2.
36 /3 width=5 by lfpx_fsge_comp, lpx_cpxs_trans, lfeq_cpx_trans, tc_lfxs_inv_lex_lfeq/ qed-.