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Proof step 5 from proof valid-eraseqd-append (previous step)

∀ m, lref. valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ q0 ∧ valid-eraseq(q0) ⊦ valid-eraseq((eqent + q0) + eq-entry(m, lref) ') ↔ ¬ m ∈ eqent + q0 ∧ valid-eraseq(eqent + q0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ m, lref. valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ q0 ∧ valid-eraseq(q0) ⊦ ¬ eqent.pnum ∈ q0 + eq-entry(m, lref) ' ∧ valid-eraseq(q0 + eq-entry(m, lref) ') ↔ ¬ m ∈ eqent ' + q0 ∧ ¬ eqent.pnum ∈ q0 ∧ valid-eraseq(q0)

Rule argument

Additional information

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