Theorems · Theorem · order theory
Setoid.lift_injective_iff_ker_eq_of_le
∀ {α : Type u_1} {β : Type u_2} {r : Setoid α} {f : α → β} (hle : r ≤ Setoid.ker f),
Function.Injective (Quotient.lift f hle) ↔ Setoid.ker f = r- Defined in
- Mathlib.Data.Setoid.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setoid.kerstatement and proof · cited by 43
- Setoid.kerLiftproof · cited by 9
- Setoid.ker_eq_lift_of_injectiveproof · cited by 4
- Setoid.kerLift_injectiveproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.