Theorems · Definition · logic and foundations
Set.offDiag
{α : Type u} → Set α → Set (α × α)The off-diagonal of a set s is the set of pairs (a, b) with a, b ∈ s and a ≠ b.
- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.ofPredproof · cited by 6,101
Cited by35
Results whose statement or proof uses this declaration.
- Set.offDiag_nonemptystatement · cited by 4
- Set.Finite.offDiagstatement · cited by 4
- Finset.coe_offDiagstatement · cited by 3
- Set.Nontrivial.einfsep_exists_of_finiteproof · cited by 2
- Set.Nontrivial.infsep_of_fintypestatement and proof · cited by 2
- Set.einfsep_of_fintypestatement and proof · cited by 2
- Finset.coe_infsepproof · cited by 2
- Set.infsep_eq_iInfstatement and proof · cited by 1
- Set.infsep_of_fintypestatement and proof · cited by 1
- Set.Nontrivial.infsep_exists_of_finiteproof · cited by 1
- Set.Finite.infsepstatement · cited by 1
- Set.offDiag_eq_emptystatement and proof · cited by 1