Theorems · Definition · group theory
Subgroup.opEquiv
{G : Type u_2} → [inst : Group G] → Subgroup G ≃o Subgroup GᵐᵒᵖA subgroup H of G determines a subgroup H.op of the opposite group Gᵐᵒᵖ.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulOppositestatement · cited by 1,135
- OrderIsostatement · cited by 874
- Subgroup.opproof · cited by 58
- Subgroup.unopproof · cited by 30
- Subgroup.op_unopproof · cited by 3
- Subgroup.op_le_op_iffproof · cited by 0
- Subgroup.unop_opproof · cited by 0
Cited by18
Results whose statement or proof uses this declaration.
- Subgroup.unop_injectiveproof · cited by 2
- Subgroup.op_injproof · cited by 2
- Subgroup.op_injectiveproof · cited by 2
- Subgroup.op_botproof · cited by 1
- Subgroup.op_sInfproof · cited by 1
- Subgroup.unop_botproof · cited by 1
- Subgroup.unop_iInfproof · cited by 0
- Subgroup.unop_iSupproof · cited by 0
- Subgroup.unop_injproof · cited by 0
- Subgroup.unop_sInfproof · cited by 0
- Subgroup.unop_sSupproof · cited by 0
- Subgroup.unop_supproof · cited by 0