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Proof step 2 from proof in-vl-in-lebrefs (previous step)

⊦ lref ∈ q0.lebrefs ↔ (∃ n. eq-entry(n, lref) ∈ q0) ∧ lref ≠ none

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ lref. lref ∈ q.lebrefs ↔ (∃ n. eq-entry(n, lref) ∈ q) ∧ lref ≠ none ⊦ lref ∈ (eqent + q).lebrefs ↔ (∃ n. eq-entry(n, lref) ∈ eqent + q) ∧ lref ≠ none

Rule argument

term: q0

Additional information

Used simplifier rules: lebrefs-base: ⊦ [].lebrefs = ∅;%queue freely generated by [], +;;% ⊦ ¬ lref ∈ ∅; (s)% ⊦ ¬ eqent ∈ []; (s)