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import Mathlib.Data.Set.Basic theorem commutativityOfIntersections (s t : Set Nat) : s ∩ t = t ∩ s := by ext x apply Iff.intro intro h1 rw [Set.mem_inter_iff, and_comm] at h1 exact h1 intro h2 rw [Set.mem_inter_iff, and_comm] at h2 -- exact h2