import Mathlib.Data.Set.Basic
import Paperproof
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 h2c