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Proof step 3 from proof valid-eraseqd-nodups-middle2 (previous step)

valid-eraseq(q0 + eq-entry(m, lref) ' + q1), m ∈ q0 + q1 ⊦

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
valid-eraseq((eqent + q) + eq-entry(m, lref) ' + q1), m ∈ (eqent + q) + q1, ∀ m, lref, q1. ¬(valid-eraseq(q + eq-entry(m, lref) ' + q1) ∧ m ∈ 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]% ⊦ eq-entry(m, lref).pnum = m; (s)