Theorems · Theorem · group theory
QuotientAddGroup.con_ker_eq_addConKer
∀ {G : Type u_1} {M : Type u_4} [inst : AddGroup G] [inst_1 : AddMonoid M] (f : G →+ M),
QuotientAddGroup.con f.ker = AddCon.ker fThe additive congruence relation defined by the kernel of an additive group homomorphism is equal to its kernel as an additive congruence relation.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddMonoidHomstatement and proof · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- AddMonoidHom.kerstatement and proof · cited by 158
- AddConstatement and proof · cited by 138
- QuotientAddGroup.leftRelproof · cited by 34
- AddCon.kerstatement and proof · cited by 24
- QuotientAddGroup.leftRel_applyproof · cited by 20
- Setoid.comm'proof · cited by 9
- AddCon.extproof · cited by 8
- QuotientAddGroup.constatement · cited by 7
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.