Theorems · Definition · logic and foundations
Set.prod
{α : Type u} → {β : Type v} → Set α → Set β → Set (α × β)The Cartesian product Set.prod s t is the set of (a, b) such that a ∈ s and b ∈ t.
- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 6 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 by7
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.prodproof · cited by 13
- ModelWithCorners.boundary_prodstatement and proof · cited by 2
- ModelWithCorners.boundary_of_boundaryless_leftstatement and proof · cited by 1
- SSet.Subcomplex.prod_objstatement · cited by 1
- SSet.iSup_subcomplexOfSimplex_prod_eq_topproof · cited by 1
- boundary_productstatement and proof · cited by 0
- ModelWithCorners.boundary_of_boundaryless_rightstatement and proof · cited by 0