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Proof step 3 from proof valid-eraseqp-valid-lebref (previous step)

valid-eraseq(apebs, q), valid-peb(v, m, apebs[n]), n ∈ q ⊦ eq-entry(n, v × m) ∈ q

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
valid-eraseq(apebs, eqent + q0), valid-peb(v, m, apebs[n]), n ∈ eqent + q0, ∀ apebs, v, m, n. valid-eraseq(apebs, q0) ∧ valid-peb(v, m, apebs[n]) ∧ n ∈ q0 → eq-entry(n, v × m) ∈ q0 ⊦ eq-entry(n, v × m) ∈ eqent + q0

Rule argument

term: q

Additional information

Used simplifier rules: queue freely generated by [], +;;% ⊦ ¬ n ∈ []; (s)