Mathlib Map

Theorems · Theorem · order theory

Setoid.mapOfSurjective_eq_map

∀ {α : Type u_1} {β : Type u_2} {r : Setoid α} {f : α → β} (h : Setoid.ker f ≤ r) (hf : Function.Surjective f),
  r.map f = r.mapOfSurjective f h hf

A special case of the equivalence closure of an equivalence relation r equaling r.

Defined in
Mathlib.Data.Setoid.Basic
Cited by
0 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Setoid.ker · cited by 43Setoid.kerSetoid.map · cited by 6Setoid.mapSetoid.eqvGen_of_setoid · cited by 2Setoid.eqvGen_of_setoidSetoid.mapOfSurjective · cited by 1Setoid.mapOfSurjectiveSetoid.mapOfSurjective_eq_mapCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.