Theorems · Theorem · order theory
Setoid.kerLift_injective
∀ {α : Type u_1} {β : Type u_2} (f : α → β), Function.Injective (Setoid.kerLift f)Given a map f from α to β, the natural map from the quotient of α by the kernel of f is injective.
- Defined in
- Mathlib.Data.Setoid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses 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.
- Quotient.mk''proof · cited by 132
- Setoid.kerstatement and proof · cited by 43
- Quotient.sound'proof · cited by 30
- Quotient.inductionOn₂'proof · cited by 19
- Setoid.kerLiftstatement and proof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- T2Quotient.compatibleproof · cited by 1
- Setoid.lift_injective_iff_ker_eq_of_leproof · cited by 0
- Setoid.quotientKerEquivRangeKerLiftproof · cited by 0