Theorems · Theorem · group theory
MonoidWithZeroHom.valueGroup_eq_range
∀ {A : Type u_1} {B : Type u_2} [inst : GroupWithZero A] [inst_1 : GroupWithZero B] (f : A →*₀ B),
Units.val '' ↑f.valueGroup = Set.range ⇑f \ {0}- Defined in
- Mathlib.Algebra.GroupWithZero.Range
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZeroGroupWithZero
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.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- Set.rangestatement · cited by 4,705
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Set.extproof · cited by 2,266
- Units.valstatement and proof · cited by 1,966
- MonoidWithZeroHomstatement and proof · cited by 704
- GroupWithZerostatement and proof · cited by 691
- Units.mk0proof · cited by 181
Cited by2
Results whose statement or proof uses this declaration.
- Valuation.exists_isUniformizer_of_isCyclic_of_nontrivialproof · cited by 2
- Valuation.IsRankOneDiscrete.generator_zpowers_eq_rangeproof · cited by 1