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Proof step 2 from proof dom-restrict (previous step)

s ⊆ dom st ⊦ dom st \ dom st \ s = s

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)
Proof step 4:
s ⊆ dom st ⊦ ∀ a. a ∈ dom st \ dom st \ s ↔ a ∈ s

Rule argument

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

Additional information

Used terms: s, dom st \ dom st \ s