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Proof step 1 from proof in-01 (conclusion)

⊦ a ∈ set2list(s) ↔ a ∈ s

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ s0, a. # s0 < # s → true → (a ∈ set2list(s0) ↔ a ∈ s0) ⊦ a ∈ set2list(s) ↔ a ∈ s

Rule argument

indvar: # s wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # s