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Proof step 8 from proof restrict-intersect-empty (previous step)

dom st ∩ s = ∅, a ∈ s ⊦ s = ∅, # s = 0, (a ∈ st \ s ↔ a ∈ st) ∧ (∅)[a] = st[a]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)
Proof step 10:
∀ a. a ∈ dom st ∩ s ↔ a ∈ ∅, a ∈ s ⊦ s = ∅, # s = 0, (a ∈ st \ s ↔ a ∈ st) ∧ (∅)[a] = st[a]

Rule argument

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

Additional information

Used terms: ∅, dom st ∩ s