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Proof step 6 from proof valid-eraseqd-nodups-middle0 (previous step)

eqent = eq-entry(m1, lref1), valid-eraseq(q + eq-entry(m, lref) ' + q1), m ∈ eqent ' + q, ∀ m0, lref0, q0. ¬ valid-eraseq(q + eq-entry(m0, lref0) ' + q0) ∨ ¬ m0 ∈ q ⊦ m1 = m, m1 ∈ q1, m1 ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
valid-eraseq(q + eq-entry(m, lref) ' + q1), m ∈ q, ∀ m0, lref0, q0. ¬ valid-eraseq(q + eq-entry(m0, lref0) ' + q0) ∨ ¬ m0 ∈ q ⊦ m1 ∈ q, m1 ∈ q1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ n ≠ n0 → (n ∈ eq-entry(n0, lref) ' + q ↔ n ∈ q); (s)