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Proof step 4 from proof valid-eraseqd-rem-middle (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
valid-eraseq(q + eqent ' + q1), ∀ eqent, q1. valid-eraseq(q + eqent ' + q1) → valid-eraseq(q + q1) ⊦ eqent0.pnum ∈ q, eqent0.pnum ∈ eqent ', eqent0.pnum ∈ q1, ¬ eqent0.pnum ∈ q + q1 ∧ valid-eraseq(q + q1)

Rule argument

Additional information

Used simplifier rules: valid-eraseqd-rec: ⊦ valid-eraseq(eqent ' + q) ↔ ¬ eqent.pnum ∈ q ∧ valid-eraseq(q);% ⊦ 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)