Theorems · Definition · group theory
AddSubgroup.orderIsoAddCon
{G : Type u_1} → [inst : AddGroup G] → { N // N.Normal } ≃o AddCon GThe normal subgroups correspond to the additive congruence relations on an AddGroup.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- OrderIsostatement · cited by 874
- AddSubgroup.Normalstatement and proof · cited by 183
- AddConstatement and proof · cited by 138
- QuotientAddGroup.conproof · cited by 7
- AddCon.addSubgroupproof · cited by 4
- QuotientAddGroup.con_addSubgroupproof · cited by 0
Cited by3
Results whose statement or proof uses this declaration.
- QuotientAddGroup.con_le_iffproof · cited by 1
- AddSubgroup.orderIsoAddCon_applystatement and proof · cited by 0
- AddSubgroup.orderIsoAddCon_symm_apply_coestatement and proof · cited by 0