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Proof step 3 from proof valid-eraseqp-update-other (previous step)

⊦ valid-eraseq(apebs[m, apeb], q) ↔ valid-eraseq(apebs, q), m ∈ q

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
∀ apebs, m, apeb. (valid-eraseq(apebs[m, apeb], q0) ↔ valid-eraseq(apebs, q0)) ∨ m ∈ q0 ⊦ valid-eraseq(apebs[m, apeb], eqent + q0) ↔ valid-eraseq(apebs, eqent + q0), m ∈ eqent + q0

Rule argument

term: q

Additional information

Used simplifier rules: valid-eraseqp-base: ⊦ valid-eraseq(apebs, []);%queue freely generated by [], +;;