Theorems · Definition
Function.surjInv
{α : Sort u} → {β : Sort v} → {f : α → β} → Function.Surjective f → β → αThe inverse of a surjective function. (Unlike invFun, this does not require
α to be inhabited.)
- Defined in
- Mathlib.Logic.Function.Basic
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by80
Results whose statement or proof uses this declaration.
- Equiv.ofBijectiveproof · cited by 70
- Matrix.det_mulproof · cited by 51
- Function.bijective_iff_has_inverseproof · cited by 50
- Function.surjInv_eqstatement · cited by 18
- Finite.of_surjectiveproof · cited by 14
- Function.injective_surjInvstatement · cited by 14
- Module.projective_lifting_propertyproof · cited by 13
- Function.rightInverse_surjInvstatement · cited by 11
- Function.Surjective.hasRightInverseproof · cited by 10
- Fintype.card_le_of_surjectiveproof · cited by 10
- Finite.injective_iff_surjectiveproof · cited by 9
- Module.Basis.sumQuotproof · cited by 8