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Proof step 18 from proof rm-vl-in-before (previous step)

∀ n, lref, lref0. eq-entry(n, lref) ∈ q0 → lref = lref0 ∨ (∃ n. eq-entry(n, lref) ∈ q0 - lref0), eq-entry(n, lref) = eq-entry(m, lref1) ∨ eq-entry(n, lref) ∈ q0 ⊦ lref = lref0, eq-entry(n, lref) ∈ q0, ∃ n0. eq-entry(n0, lref) ∈ (lref1 = lref0 ⊃ q0 - lref0;eq-entry(m, lref1) ' + (q0 - lref0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
∀ n, lref, lref0. eq-entry(n, lref) ∈ q0 → lref = lref0 ∨ (∃ n. eq-entry(n, lref) ∈ q0 - lref0) ⊦ lref = lref0, eq-entry(m, lref) ∈ q0, ∃ n0. n0 = m ∨ eq-entry(n0, lref) ∈ q0 - lref0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ eqent ∈ eqent0 ' + q ↔ eqent = eqent0 ∨ eqent ∈ q; (s)% ⊦ eq-entry(m, lref) = eq-entry(m0, lref0) ↔ m = m0 ∧ lref = lref0; (ws)