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Proof step 3 from proof valid-eraseqd-rem-middle (previous step)

valid-eraseq(q0 + eqent ' + q1) ⊦ valid-eraseq(q0 + q1)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
valid-eraseq((eqent0 + q) + eqent ' + q1), ∀ eqent, q1. valid-eraseq(q + eqent ' + q1) → valid-eraseq(q + q1) ⊦ valid-eraseq((eqent0 + q) + q1)

Rule argument

term: q0

Additional information

Used simplifier rules: valid-eraseqd-rec: ⊦ valid-eraseq(eqent ' + q) ↔ ¬ eqent.pnum ∈ q ∧ valid-eraseq(q);%queue freely generated by [], +;;% ⊦ [] + q = q; (s)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]