Theorems · Definition
Equiv.ofBijective
{α : Sort u} → {β : Sort v} → (f : α → β) → Function.Bijective f → α ≃ βIf f is a bijective function, then its domain is equivalent to its codomain.
- Defined in
- Mathlib.Logic.Equiv.Defs
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses Classical.choice
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.
- Equivstatement · cited by 8,337
- Function.Bijectivestatement and proof · cited by 863
- Function.Bijective.surjectiveproof · cited by 114
- Function.surjInvproof · cited by 63
- Function.leftInverse_surjInvproof · cited by 2
Cited by146
Results whose statement or proof uses this declaration.
- Matrix.det_mulproof · cited by 51
- IsLocalizedModule.isoproof · cited by 34
- Subgroup.IsComplement.equivproof · cited by 34
- RingEquiv.ofBijectiveproof · cited by 24
- Module.End.isUnit_iffproof · cited by 21
- IsHomeomorph.homeomorphproof · cited by 18
- Subgroup.IsComplement.leftQuotientEquivproof · cited by 17
- CategoryTheory.isIso_iff_bijectiveproof · cited by 16
- CategoryTheory.Abelian.Ext.homEquiv₀proof · cited by 13
- Fintype.sum_bijectiveproof · cited by 13
- finEquivPowersproof · cited by 9
- Equiv.ofBijective_applystatement and proof · cited by 9