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Proof step 6 from proof lebrefs-append-lref (previous step)

lref = none, ∀ n, v, m. (q0 + eq-entry(n, v × m) ').lebrefs = q0.lebrefs ++ (v × m) ⊦ (q0 + eq-entry(n, v × m) ').lebrefs ∪ (lref ≠ none ⊃ ∅ ++ lref;∅) = (q0.lebrefs ∪ (lref ≠ none ⊃ ∅ ++ lref;∅)) ++ (v × m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ n, v, m. (q0 + eq-entry(n, v × m) ').lebrefs = q0.lebrefs ++ (v × m) ⊦ (q0 + eq-entry(n, v × m) ').lebrefs = q0.lebrefs ++ (v × m)

Rule argument

Additional information

Used simplifier rules: unc: ⊦ s1 ∪ s2 = s2 ∪ s1; from specification set-union[lebrefset]%una: ⊦ (s2 ∪ s3) ∪ s4 = s2 ∪ s3 ∪ s4; from specification set-union[lebrefset]% ⊦ s0 ∪ ∅ = s0; (s)