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Proof step 13 from proof sub-one (previous step)

∀ a1. ¬ a1 ∈ s ⊦ # s = 0, s = ∅, a ∈ s

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)
Proof step 15:
∀ a1. ¬ a1 ∈ s ⊦ # s = 0, a ∈ s, ∀ a. a ∈ s ↔ a ∈ ∅

Rule argument

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

Additional information

Used terms: ∅, s