Theorems · Definition · group theory
AddSubgroup.equivOp
{G : Type u_2} → [inst : AddGroup G] → (H : AddSubgroup G) → ↥H ≃ ↥H.opBijection between an additive subgroup H and its opposite.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddOppositestatement · cited by 452
- AddSubgroup.opstatement · cited by 57
- Equiv.subtypeEquivproof · cited by 32
- AddOpposite.opEquivproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- QuotientAddGroup.leftRel_applyproof · cited by 20
- isAddFundamentalDomain_Ioc'proof · cited by 2
- AddSubgroup.equivOp_apply_coestatement and proof · cited by 0
- AddSubgroup.equivOp_symm_apply_coestatement and proof · cited by 0
- AddSubgroup.properlyDiscontinuousVAdd_opposite_of_tendsto_cofiniteproof · cited by 0