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Proof step 5 from proof lebrefs-lref (previous step)

⊦ (eq-entry(n, v × m) ' + []).lebrefs = ∅ ++ (v × m)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: lebrefs-rec seq: ⊦ (eqent ' + q).lebrefs = q.lebrefs ∪ (eqent.lebref ≠ none ⊃ {eqent.lebref} ;∅) subst: [q, eqent] → [[], eq-entry(n, v × m)] flags: <all paths>

Additional information

Used simplifier rules: lebrefs-base: ⊦ [].lebrefs = ∅;% ⊦ eq-entry(m, lref).lebref = lref; (s)% ⊦ none ≠ v × m; (s)% ⊦ {lref} = ∅ ++ lref; (s)% ⊦ (s1 ++ lref) ∪ s2 = (s1 ∪ s2) ++ lref; (s)% ⊦ s0 ∪ ∅ = s0; (s)%una: ⊦ (s2 ∪ s3) ∪ s4 = s2 ∪ s3 ∪ s4; from specification set-union[lebrefset]%unc: ⊦ s1 ∪ s2 = s2 ∪ s1; from specification set-union[lebrefset] Used terms: [], eq-entry(n, v × m)