Theorems · Definition · group theory
Subgroup.equivOp
{G : Type u_2} → [inst : Group G] → (H : Subgroup G) → ↥H ≃ ↥H.opBijection between a subgroup H and its opposite.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- Group
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulOppositestatement · cited by 1,135
- Subgroup.opstatement · cited by 58
- Equiv.subtypeEquivproof · cited by 32
- MulOpposite.opEquivproof · cited by 24
Cited by4
Results whose statement or proof uses this declaration.
- QuotientGroup.leftRel_applyproof · cited by 17
- Subgroup.equivOp_apply_coestatement and proof · cited by 0
- Subgroup.equivOp_symm_apply_coestatement and proof · cited by 0
- Subgroup.properlyDiscontinuousSMul_opposite_of_tendsto_cofiniteproof · cited by 0