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Proof step 2 from proof rmdup (previous step)

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

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
⊦ (∀ a. a ∈ rmdup(x) → a ∈ []) ↔ (∀ a. a ∈ x → a ∈ [])
Proof step 9:
∀ x. (∀ a. a ∈ rmdup(x) → a ∈ y0) ↔ (∀ a. a ∈ x → a ∈ y0) ⊦ (∀ a0. a0 ∈ rmdup(x) → a0 ∈ a + y0) ↔ (∀ a0. a0 ∈ x → a0 ∈ a + y0)

Rule argument

term: y

Additional information

Used simplifier rules: list freely generated by [], +;;