Theorems · Theorem · group theory
QuotientGroup.induction_on
∀ {α : Type u_1} [inst : Group α] {s : Subgroup α} {C : α ⧸ s → Prop} (x : α ⧸ s), (∀ (z : α), C ↑z) → C x- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- QuotientGroup.mkstatement and proof · cited by 196
- Quotient.inductionOn'proof · cited by 69
Cited by17
Results whose statement or proof uses this declaration.
- QuotientGroup.monoidHom_extproof · cited by 5
- Abelianization.hom_extproof · cited by 4
- CommGroup.isMulTorsion_quotient_range_powMonoidHomproof · cited by 2
- Subgroup.normalCore_eq_kerproof · cited by 1
- FixedPoints.toAlgAut_surjectiveproof · cited by 1
- QuotientGroup.orbit_eq_out_smulproof · cited by 1
- QuotientGroup.map_id_applyproof · cited by 1
- QuotientGroup.map_mapproof · cited by 1
- ClassGroup.inductionproof · cited by 1
- FixedPoints.minpoly.of_eval₂proof · cited by 1
- ModularGroup.exists_bound_of_subgroup_invariant_of_isBigOproof · cited by 1
- groupCohomology.H1InfRes_exactproof · cited by 0