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Proof step 2 from proof empty (previous step)

⊦ # ∅.keys = 0, ∅.keys = ∅

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 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] → [∅, ∅.keys] flags: <all paths>

Additional information

Used simplifier rules: Keys: ⊦ a ∈ st.keys ↔ a ∈ st;% ⊦ ¬ a ∈ ∅; (s)% ⊦ ¬ a ∈ ∅; (s) Used terms: ∅, ∅.keys