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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 *)
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11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/rt_transition/lfpx_aaa.ma".
16 include "basic_2/rt_transition/lfpr_lfpx.ma".
18 (* PARALLEL R-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES ****************)
20 (* Properties with atomic arity assignment for terms ************************)
22 lemma cpr_aaa_conf: ∀h,G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A →
23 ∀T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
24 /3 width=5 by cpx_aaa_conf, cpm_fwd_cpx/ qed-.
26 lemma lfpr_aaa_conf: ∀h,G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A →
27 ∀L2. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → ⦃G, L2⦄ ⊢ T ⁝ A.
28 /3 width=4 by lfpx_aaa_conf, lfpr_fwd_lfpx/ qed-.