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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/computation/lfprs_aaa.ma".
16 include "basic_2/equivalence/lfpcs_lfpcs.ma".
18 (* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
20 (* Main properties about atomic arity assignment on terms *******************)
22 theorem aaa_lfpcs_mono: ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ →
23 ∀T,A1. L1 ⊢ T ⁝ A1 → ∀A2. L2 ⊢ T ⁝ A2 →
25 #L1 #L2 #HL12 #T #A1 #HT1 #A2 #HT2
26 elim (lfpcs_inv_lfprs … HL12) -HL12 #L #HL1 #HL2
27 lapply (aaa_lfprs_conf … HT1 … HL1) -L1 #HT1
28 lapply (aaa_lfprs_conf … HT2 … HL2) -L2 #HT2
29 lapply (aaa_mono … HT1 … HT2) -L -T //