Theorems · Theorem · group theory
MonoidWithZeroHom.valueGroup_def
∀ {A : Type u_1} {B : Type u_2} [inst : MonoidWithZero A] [inst_1 : MonoidWithZero B] (f : A →*₀ B),
f.valueGroup = Subgroup.closure ↑f.valueMonoid- Defined in
- Mathlib.Algebra.GroupWithZero.Range
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZeroMonoidWithZero
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.
- SetLike.coestatement · cited by 8,199
- Subgroupstatement · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement · cited by 2,804
- MonoidWithZeroHomstatement and proof · cited by 704
- MonoidWithZerostatement and proof · cited by 456
- Subgroup.closurestatement · cited by 196
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.valueMonoidstatement · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- MonoidWithZeroHom.valueMonoid_eq_valueGroupproof · cited by 1