Theorems · Theorem · group theory
AddMonoid.Coprod.range_eq
∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] {K : Type u_3} [inst_2 : AddGroup K]
(f : AddMonoid.Coprod G H →+ K), f.range = (f.comp AddMonoid.Coprod.inl).range ⊔ (f.comp AddMonoid.Coprod.inr).range- Defined in
- Mathlib.GroupTheory.Coprod.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidHom.compstatement and proof · cited by 339
- AddSubgroup.mapproof · cited by 189
- AddMonoidHom.rangestatement and proof · cited by 142
- AddMonoid.Coprodstatement and proof · cited by 104
- AddMonoid.Coprod.inlstatement and proof · cited by 42
- AddMonoid.Coprod.inrstatement and proof · cited by 42
- AddMonoidHom.range_eq_mapproof · cited by 15
- AddMonoidHom.map_rangeproof · cited by 5
- AddSubgroup.map_supproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddMonoid.Coprod.range_liftproof · cited by 0