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Proof step 3 from proof perm-all (previous step)

⊦ x ⊆m y ∧ y ⊆m x ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ (∀ a. #oc(a, x) ≤ #oc(a, y)) ∧ (∀ a. #oc(a, y) ≤ #oc(a, x)) ↔ (∀ a. a ∈ x ∨ a ∈ y → #oc(a, x) = #oc(a, y))

Rule argument

Additional information

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