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Proof step 14 from proof rmdup (previous step)

a0 ∈ rmdup(x), ∀ a0. a0 ∈ x → a0 = a ∨ a0 ∈ y0, ∀ x. (∀ a. a ∈ rmdup(x) → a ∈ y0) ↔ (∀ a. a ∈ x → a ∈ y0) ⊦ a0 = a, a0 ∈ y0

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: a0

Additional information

Used simplifier rules: rm-in-01: ⊦ a ∈ rmdup(x) → a ∈ x; (forward) from specification list-dup Used terms: a0