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theorem proved term proof

structured_set_singleton

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formal statement (Lean)

 157theorem structured_set_singleton : StructuredSet = {1} := by

proof body

Term-mode proof.

 158  ext x
 159  simp only [StructuredSet, Set.mem_setOf_eq, Set.mem_singleton_iff]
 160  constructor
 161  · intro ⟨hpos, hdef⟩; exact (defect_zero_iff_one hpos).mp hdef
 162  · intro h; subst h; exact ⟨one_pos, defect_at_one⟩
 163
 164/-- Membership in structured set ⟺ existence. -/

depends on (3)

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