Theorems · Definition · order theory
Setoid.quotientKerEquivRangeKerLift
{α : Type u_1} → {β : Type u_2} → (f : α → β) → Quotient (Setoid.ker f) ≃ ↑(Set.range (Setoid.kerLift f))The quotient of α by the kernel of a function f
bijects with the image of f lifted to the quotient.
- Defined in
- Mathlib.Data.Setoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Equiv.ofInjectiveproof · cited by 64
- Setoid.kerstatement · cited by 43
- Setoid.kerLiftstatement and proof · cited by 9
- Setoid.kerLift_injectiveproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Setoid.quotientKerEquivRangeproof · cited by 2