Theorems · Theorem · group theory
Subgroup.map_le_range
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] (f : G →* N) (H : Subgroup G),
Subgroup.map f H ≤ f.range- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- le_topproof · cited by 411
- MonoidHom.rangestatement · cited by 314
- Subgroup.mapstatement · cited by 301
- MonoidHom.range_eq_mapproof · cited by 37
- Subgroup.map_monoproof · cited by 8
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.index_mapproof · cited by 6
- Subgroup.map_subtype_leproof · cited by 5
- MonoidHom.ker_transferSylow_isComplement'proof · cited by 3
- alternatingGroup.mem_map_kleinFour_ofSubtypeproof · cited by 1
- NumberField.IsCMField.indexRealUnits_eq_two_iffproof · cited by 0