enrich finite-authentic-names , Mondex-AOP with functions Σ : (name → nat) × nameset → nat; axioms sum-empty : ⊦ Σ(balance, ∅) = 0; used for : s, ls; sum-insert : ⊦ Σ(balance, nas ++ na) = ((na ∈ nas ⊃ Σ(balance, nas); balance(na) + Σ(balance, nas))); used for : s, ls; end enrich