1 (**************************************************************************)
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 *)
11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/computation/lcprs_aaa.ma".
16 include "basic_2/equivalence/cpcs_cpcs.ma".
17 include "basic_2/equivalence/lcpcs_lcpcs.ma".
19 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL EBVIRONMENTS *************)
21 (* Main properties about atomic arity assignment on terms *******************)
23 theorem aaa_lcpcs_mono: ∀L1,L2. L1 ⊢ ⬌* L2 →
24 ∀T,A1. L1 ⊢ T ⁝ A1 → ∀A2. L2 ⊢ T ⁝ A2 →
26 #L1 #L2 #HL12 #T #A1 #HT1 #A2 #HT2
27 elim (lcpcs_inv_lcprs … HL12) -HL12 #L #HL1 #HL2
28 lapply (aaa_lcprs_conf … HT1 … HL1) -L1 #HT1
29 lapply (aaa_lcprs_conf … HT2 … HL2) -L2 #HT2
30 lapply (aaa_mono … HT1 … HT2) -L -T //
33 theorem aaa_cpcs_mono: ∀L,T1,T2. L ⊢ T1 ⬌* T2 →
34 ∀A1. L ⊢ T1 ⁝ A1 → ∀A2. L ⊢ T2 ⁝ A2 →
36 #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
37 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
38 lapply (aaa_cprs_conf … HA1 … HT1) -T1 #HA1
39 lapply (aaa_cprs_conf … HA2 … HT2) -T2 #HA2
40 lapply (aaa_mono … HA1 … HA2) -L -T //