Theorems · Definition · group theory
QuotientAddGroup.con
{G : Type u_1} → [inst : AddGroup G] → (N : AddSubgroup G) → [nN : N.Normal] → AddCon GThe additive congruence relation generated by a normal additive subgroup.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddSubgroup.Normalstatement and proof · cited by 183
- AddConstatement · cited by 138
- QuotientAddGroup.leftRelproof · cited by 34
Cited by10
Results whose statement or proof uses this declaration.
- QuotientAddGroup.liftproof · cited by 15
- AddSubgroup.orderIsoAddConproof · cited by 3
- QuotientAddGroup.lift_surjective_of_surjectiveproof · cited by 2
- QuotientAddGroup.con_le_iffstatement · cited by 1
- AddSubgroup.orderIsoAddCon_applystatement · cited by 0
- Ideal.Quotient.ringConproof · cited by 0
- AddCon.addSubgroup_quotientAddGroupConstatement · cited by 0
- QuotientAddGroup.con_addSubgroupstatement · cited by 0
- QuotientAddGroup.con_ker_eq_addConKerstatement · cited by 0
- QuotientAddGroup.con_monostatement · cited by 0