Theorems · Definition · logic and foundations
Equiv.Set.prod
{α : Type u_3} → {β : Type u_4} → (s : Set α) → (t : Set β) → ↑(s ×ˢ t) ≃ ↑s × ↑tThe set product of two sets is equivalent to the type product of their coercions to types.
- Defined in
- Mathlib.Logic.Equiv.Set
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- SProd.sprodstatement · cited by 1,750
- Equiv.subtypeProdEquivProdproof · cited by 0
Cited by22
Results whose statement or proof uses this declaration.
- Homeomorph.Set.prodproof · cited by 7
- Set.Countable.prodproof · cited by 6
- Sublattice.prodEquivproof · cited by 3
- biInf_sup_biInfproof · cited by 2
- biSup_inf_biSupproof · cited by 2
- Cardinal.mk_setProdproof · cited by 2
- LinearIndepOn.tmul_of_isDomainproof · cited by 1
- Subgroup.prodEquivproof · cited by 1
- AddSubgroup.prodEquivproof · cited by 1
- Set.encard_prodproof · cited by 1
- Sublattice.prodEquiv_toEquivstatement · cited by 0
- Submonoid.prodEquivproof · cited by 0