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Proof step 3 from proof rmdup (previous step)

⊦ (∀ a. a ∈ rmdup(x) → a ∈ []) ↔ (∀ a. a ∈ x → a ∈ [])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ (∀ a. ¬ a ∈ rmdup(x)) ↔ (∀ a. ¬ a ∈ x)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ []; (s)