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Proof step 3 from proof rm-vl-in-before (previous step)

eq-entry(n, lref) ∈ q ⊦ lref = lref0, ∃ n. eq-entry(n, lref) ∈ q - lref0

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
eq-entry(n, lref) ∈ eqent + q0, ∀ n, lref, lref0. eq-entry(n, lref) ∈ q0 → lref = lref0 ∨ (∃ n. eq-entry(n, lref) ∈ q0 - lref0) ⊦ lref = lref0, ∃ n. eq-entry(n, lref) ∈ eqent + q0 - lref0

Rule argument

term: q

Additional information

Used simplifier rules: queue freely generated by [], +;;% ⊦ ¬ eqent ∈ []; (s)