Theorems · Theorem · order theory
Set.singleton_prod_singleton
∀ {α : Type u_1} {β : Type u_2} {a : α} {b : β}, {a} ×ˢ {b} = {(a, b)}- Defined in
- Mathlib.Data.Set.Prod
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.extproof · cited by 2,266
- SProd.sprodstatement · cited by 1,750
Cited by9
Results whose statement or proof uses this declaration.
- Ideal.prod_bot_botproof · cited by 2
- Submonoid.bot_prod_botproof · cited by 1
- AddSubmonoid.bot_prod_botproof · cited by 1
- Subgroup.bot_prod_botproof · cited by 1
- AddSubgroup.bot_prod_botproof · cited by 1
- MeasureTheory.SimpleFunc.pair_preimage_singletonproof · cited by 1
- TopologicalSpace.Compacts.singleton_prod_singletonproof · cited by 0
- TopologicalSpace.Closeds.singleton_prod_singletonproof · cited by 0
- TopologicalSpace.NonemptyCompacts.singleton_prod_singletonproof · cited by 0