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.
- DiscreteUniformity.eq_pure_of_cauchyproof · cited by 1