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Proof step 1 from proof dom-union-l (conclusion)

⊦ dom(st0 ⊕ st1) = dom st0 ∪ dom st1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)
Proof step 3:
⊦ ∀ a. a ∈ dom(st0 ⊕ st1) ↔ a ∈ dom st0 ∪ dom st1

Rule argument

spec: set-basic inst: name: Extension seq: ⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2) subst: [s2, s1] → [dom st0 ∪ dom st1, dom(st0 ⊕ st1)] flags: rewrite

Additional information

Used terms: dom st0 ∪ dom st1, dom(st0 ⊕ st1)