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Proof step 3 from proof valid-eraseq-stronger-next-append-none (previous step)

m < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), q) ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), q + eq-entry(m, none) ') ↔ ¬ valid-peb(apebs[m])

User applied rule structural induction

And obtained the following new goals

Proof step 4:
m < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), []) ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), [] + eq-entry(m, none) ') ↔ ¬ valid-peb(apebs[m])
Proof step 7:
m < # apebs, valid-eraseq-stronger(subarray(apebs, 0, m), eqent + q0), ∀ m, apebs. m < # apebs ∧ valid-eraseq-stronger(subarray(apebs, 0, m), q0) → (valid-eraseq-stronger(subarray(apebs, 0, m + 1), q0 + eq-entry(m, none) ') ↔ ¬ valid-peb(apebs[m])) ⊦ valid-eraseq-stronger(subarray(apebs, 0, m + 1), (eqent + q0) + eq-entry(m, none) ') ↔ ¬ valid-peb(apebs[m])

Rule argument

indvar: q

Additional information

Used simplifier rules: queue freely generated by [], +;;