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Proof step 17 from proof size-exgr (previous step)

a ∈ s0, ∀ s. # s ≠ 0 → (∃ a0. a0 ∈ s) ⊦ # s0 = 1, # s0 = 0, ∃ a0. a0 ∈ s0 ∧ a0 ≠ a

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ a ∈ s ↔ (∃ s0. s = s0 ++ a ∧ ¬ a ∈ s0)
Proof step 19:
∀ s. # s ≠ 0 → (∃ a0. a0 ∈ s), ∃ s1. s0 = s1 ++ a ∧ ¬ a ∈ s1 ⊦ # s0 = 0, # s0 = 1, ∃ a0. a0 ∈ s0 ∧ a0 ≠ a

Rule argument

spec: <toplevel> name: indef seq: ⊦ a ∈ s ↔ (∃ s0. s = s0 ++ a ∧ ¬ a ∈ s0) subst: [s, a] → [s0, a] flags: <all paths>

Additional information

Used terms: s0, a