Theorems · Theorem · group theory
QuotientGroup.ker_le_range_iff
∀ {G : Type u_1} {H : Type u_2} {I : Type u_3} [inst : Group G] [inst_1 : Group H] [inst_2 : MulOneClass I] (f : G →* H)
[inst_3 : f.range.Normal] (g : H →* I), g.ker ≤ f.range ↔ (QuotientGroup.mk' f.range).comp g.ker.subtype = 1- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- MulOneClassstatement and proof · cited by 1,018
- MonoidHom.compstatement and proof · cited by 469
- Subgroup.Normalstatement and proof · cited by 334
- MonoidHom.rangestatement and proof · cited by 314
- DFunLike.congr_funproof · cited by 288
- MonoidHom.kerstatement and proof · cited by 212
- Subgroup.subtypestatement and proof · cited by 185
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.