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Theorems · Theorem · order theory

SetRel.exists_eq_singleton_of_prod_subset_id

∀ {α : Type u_1} {s t : Set α}, s.Nonempty → t.Nonempty → s ×ˢ t ⊆ SetRel.id → ∃ x, s = {x} ∧ t = {x}
Defined in
Mathlib.Data.Rel
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Setstatement and proof · cited by 53,352
  • Set.Nonemptystatement and proof · cited by 2,627
  • SProd.sprodstatement and proof · cited by 1,750
  • SetRel.idstatement and proof · cited by 33

Cited by1

Results whose statement or proof uses this declaration.