Theorems · Definition · group theory
Subgroup.op
{G : Type u_2} → [inst : Group G] → Subgroup G → Subgroup GᵐᵒᵖPull a subgroup back to an opposite subgroup along MulOpposite.unop
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 26 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.
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.preimageproof · cited by 4,946
- Subgroupstatement and proof · cited by 3,593
- MulOppositestatement · cited by 1,135
- MulOpposite.unopproof · cited by 268
- Subgroup.one_memproof · cited by 31
Cited by62
Results whose statement or proof uses this declaration.
- QuotientGroup.leftRelproof · cited by 61
- Subgroup.opEquivproof · cited by 18
- Subgroup.equivOpstatement · cited by 4
- Subgroup.normal_opstatement · cited by 3
- Subgroup.op_unopstatement · cited by 3
- QuotientGroup.soundstatement and proof · cited by 2
- Subgroup.op_closurestatement · cited by 2
- Subgroup.op_injstatement · cited by 2
- Subgroup.op_injectivestatement · cited by 2
- MeasureTheory.QuotientMeasureEqMeasurePreimage.mulInvariantMeasure_quotientstatement and proof · cited by 2
- MeasureTheory.Measure.IsMulLeftInvariant.quotientMeasureEqMeasurePreimage_of_setstatement and proof · cited by 2
- Subgroup.mem_opstatement · cited by 2