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Proof step 1 from proof nodups (conclusion)

∀ a. a ∈ x ↔ a ∈ y, ¬ dups(x), ¬ dups(y) ⊦ perm(x, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
∀ a. a ∈ x ↔ a ∈ y ⊦ dups(y), dups(x), x ⊆m y ∧ y ⊆m x

Rule argument

Additional information

Used simplifier rules: perm-def: ⊦ perm(x, y) ↔ ¬ ¬(x ⊆m y ∧ y ⊆m x);