Theorems · Theorem · order theory
Setoid.range_kerLift_eq_range
∀ {α : Type u_1} {β : Type u_2} (f : α → β), Set.range (Setoid.kerLift f) = Set.range fThe image of f lifted to the quotient by its kernel is equal to the image of f itself.
- Defined in
- Mathlib.Data.Setoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
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 · cited by 53,352
- Set.rangestatement · cited by 4,705
- Setoid.kerstatement · cited by 43
- Setoid.kerLiftstatement · cited by 9
- Set.range_quotient_liftproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Setoid.quotientKerEquivRangeproof · cited by 2