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Proof step 2 from proof toSet-empty (previous step)

⊦ # [].toSet = 0, [].toSet = ∅

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:
⊦ a ∈ x.toSet ↔ a ∈ x

Rule argument

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

Additional information

Used simplifier rules: toSet-ext: ⊦ a ∈ x.toSet ↔ a ∈ x;% ⊦ ¬ a ∈ []; (s)% ⊦ ¬ a ∈ ∅; (s) Used terms: ∅, [].toSet