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Proof step 4 from proof valid-eraseqd-nodups-middle0 (previous step)

valid-eraseq((eqent + q) + eq-entry(m, lref) ' + q1), m ∈ eqent + q, ∀ m, lref, q1. ¬(valid-eraseq(q + eq-entry(m, lref) ' + q1) ∧ m ∈ q) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
valid-eraseq(q + eq-entry(m, lref) ' + q1), m ∈ eqent ' + q, ∀ m0, lref0, q0. ¬ valid-eraseq(q + eq-entry(m0, lref0) ' + q0) ∨ ¬ m0 ∈ q ⊦ eqent.pnum = m, eqent.pnum ∈ q, eqent.pnum ∈ q1

Rule argument

Additional information

Used simplifier rules: valid-eraseqd-rec: ⊦ valid-eraseq(eqent ' + q) ↔ ¬ eqent.pnum ∈ q ∧ valid-eraseq(q);% ⊦ n ∈ eq-entry(n0, lref) ' + q ↔ n ∈ q ∨ n = n0; (ss)% ⊦ n ∈ q0 + q1 ↔ n ∈ q0 ∨ n ∈ q1; (ss)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ eqent + q = eqent ' + q; (s)