Theorems · Theorem · group theory
AddMonoid.Coprod.mrange_eq
∀ {M : Type u_1} {N : Type u_2} {P : Type u_5} [inst : AddZeroClass M] [inst_1 : AddZeroClass N]
[inst_2 : AddZeroClass P] (f : AddMonoid.Coprod M N →+ P),
AddMonoidHom.mrange f =
AddMonoidHom.mrange (f.comp AddMonoid.Coprod.inl) ⊔ AddMonoidHom.mrange (f.comp AddMonoid.Coprod.inr)- Defined in
- Mathlib.GroupTheory.Coprod.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidHomstatement and proof · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- AddSubmonoidstatement and proof · cited by 1,178
- AddMonoidHom.compstatement and proof · cited by 339
- AddMonoid.Coprodstatement and proof · cited by 104
- AddSubmonoid.mapproof · cited by 99
- AddMonoidHom.mrangestatement and proof · cited by 61
- AddMonoid.Coprod.inlstatement and proof · cited by 42
- AddMonoid.Coprod.inrstatement and proof · cited by 42
- AddMonoidHom.mrange_eq_mapproof · cited by 15
- AddSubmonoid.map_supproof · cited by 4
- AddMonoidHom.map_mrangeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoid.Coprod.mrange_liftproof · cited by 0