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Proof step 1 from proof dom-del (conclusion)

⊦ dom(st -- a) = dom st -- a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)

Rule argument

spec: set-basic name: Extension seq: ⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2) subst: [s2, s1] → [dom st -- a, dom(st -- a)] flags: <all paths>

Additional information

Used simplifier rules: Dom: ⊦ a ∈ dom st ↔ a ∈ st;% ⊦ a ∈ s -- b ↔ a ≠ b ∧ a ∈ s; (s)% ⊦ a ∈ st -- b ↔ a ≠ b ∧ a ∈ st; (ws) Used terms: dom st -- a, dom(st -- a)