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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/scpds_aaa.ma".
16 include "basic_2/equivalence/scpes.ma".
18 (* DECOMPOSED EXTENDED PARALLEL EQUIVALENCE FOR TERMS ***********************)
20 (* Main inversion lemmas about atomic arity assignment on terms *************)
22 theorem scpes_aaa_mono: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
23 ∀A1. ⦃G, L⦄ ⊢ T1 ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T2 ⁝ A2 →
25 #h #o #G #L #T1 #T2 #d1 #d2 * #T #HT1 #HT2 #A1 #HA1 #A2 #HA2
26 lapply (scpds_aaa_conf … HA1 … HT1) -T1 #HA1
27 lapply (scpds_aaa_conf … HA2 … HT2) -T2 #HA2
28 lapply (aaa_mono … HA1 … HA2) -L -T //