Theorems · Theorem · group theory
MonoidHom.apply_ofInjective_symm
∀ {G : Type u_1} [inst : Group G] {N : Type u_5} [inst_1 : Group N] {f : G →* N} (hf : Function.Injective ⇑f)
(x : ↥f.range), f ((MonoidHom.ofInjective hf).symm x) = ↑x- Defined in
- Mathlib.Algebra.Group.Subgroup.Ker
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement · cited by 3,593
- MulEquivstatement · cited by 1,142
- MulEquiv.symmstatement · cited by 482
- MonoidHom.rangestatement and proof · cited by 314
- MulEquiv.apply_symm_applyproof · cited by 37
- MonoidHom.ofInjectivestatement and proof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- Monoid.PushoutI.NormalWord.prod_consproof · cited by 2
- Monoid.PushoutI.NormalWord.prod_summand_smulproof · cited by 1
- Monoid.PushoutI.NormalWord.cons_eq_smulproof · cited by 1
- GroupExtension.inl_conjAct_commproof · cited by 0