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Proof step 2 from proof rmdup-01 (previous step)

⊦ (∀ a. a ∈ x → a ∈ rmdup(y)) ↔ (∀ a. a ∈ x → a ∈ y)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ x. (∀ a. a ∈ x → a ∈ rmdup(y0)) ↔ (∀ a. a ∈ x → a ∈ y0) ⊦ (∀ a0. a0 ∈ x → a0 ∈ rmdup(a + y0)) ↔ (∀ a0. a0 ∈ x → a0 ∈ a + y0)

Rule argument

term: y

Additional information

Used simplifier rules: list freely generated by [], +;;%rmdup-e: ⊦ rmdup([]) = []; from specification list-dup%in-empty: ⊦ ¬ a ∈ []; from specification list