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Proof step 1 from proof in (conclusion)

⊦ a ∈ y ∧ ¬ a ∈ x → ¬ perm(x, y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ∈ y, ∀ a. #oc(a, x) ≤ #oc(a, y), ∀ a. #oc(a, y) ≤ #oc(a, x) ⊦ a ∈ x

Rule argument

Additional information

Used simplifier rules: perm: ⊦ perm(x, y) ↔ x ⊆m y ∧ y ⊆m x;%msubset: ⊦ x ⊆m y ↔ (∀ a. #oc(a, x) ≤ #oc(a, y));