Theorems · Theorem · group theory
MonoidWithZeroHom.mem_valueMonoid
∀ {A : Type u_1} {B : Type u_2} [inst : MonoidWithZero A] [inst_1 : MonoidWithZero B] (f : A →*₀ B) {b : Bˣ},
↑b ∈ Set.range ⇑f → b ∈ f.valueMonoid- Defined in
- Mathlib.Algebra.GroupWithZero.Range
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- 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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- MonoidWithZeroHomstatement and proof · cited by 704
- MonoidWithZerostatement and proof · cited by 456
- MonoidWithZeroHom.valueMonoidstatement · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- MonoidWithZeroHom.mem_valueGroupproof · cited by 4