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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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15 include "basic_2/computation/cprs_aaa.ma".
16 include "basic_2/equivalence/cpcs_cpcs.ma".
18 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
20 (* Main properties about atomic arity assignment on terms *******************)
22 theorem aaa_cpcs_mono: ∀L,T1,T2. L ⊢ T1 ⬌* T2 →
23 ∀A1. L ⊢ T1 ⁝ A1 → ∀A2. L ⊢ T2 ⁝ A2 →
25 #L #T1 #T2 #HT12 #A1 #HA1 #A2 #HA2
26 elim (cpcs_inv_cprs … HT12) -HT12 #T #HT1 #HT2
27 lapply (aaa_cprs_conf … HA1 … HT1) -T1 #HA1
28 lapply (aaa_cprs_conf … HA2 … HT2) -T2 #HA2
29 lapply (aaa_mono … HA1 … HA2) -L -T //