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Proof step 4 from proof dom-union-l (previous step)

⊦ a ∈ st0 ⊕ st1 ↔ a ∈ dom st0 ∪ dom st1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ a ∈ s1 ∪ s2 ↔ a ∈ s1 ∨ a ∈ s2

Rule argument

spec: set-union inst: name: Union seq: ⊦ a ∈ s1 ∪ s2 ↔ a ∈ s1 ∨ a ∈ s2 subst: [s2, s1, a] → [dom st1, dom st0, a] flags: rewrite

Additional information

Used simplifier rules: Dom: ⊦ a ∈ dom st ↔ a ∈ st;%oplus-l-in: ⊦ a ∈ st0 ⊕ st1 ↔ a ∈ st0 ∨ a ∈ st1; Used terms: dom st1, dom st0, a