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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
∀ n, lref, lref0. eq-entry(n, lref) ∈ q0 - lref0 → (∃ n. eq-entry(n, lref) ∈ q0) ⊦ lref1 = lref0, eq-entry(m, lref1) ∈ q0 - lref0, ∃ n0. n0 = m ∨ eq-entry(n0, lref1) ∈ q0

Rule argument

Additional information

Used simplifier rules: ⊦ eq-entry(m, lref) = eq-entry(m0, lref0) ↔ m = m0 ∧ lref = lref0; (ws)