Theorems · Theorem · group theory
MonoidWithZeroHom.mem_valueMonoid_iff
∀ {A : Type u_1} {B : Type u_2} [inst : MonoidWithZero A] [inst_1 : MonoidWithZero B] (f : A →*₀ B) {b : Bˣ},
b ∈ f.valueMonoid ↔ b ∈ Units.val ⁻¹' Set.range ⇑f- Defined in
- Mathlib.Algebra.GroupWithZero.Range
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- MonoidWithZeroMonoidWithZero
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Set.preimagestatement · cited by 4,946
- Set.rangestatement · cited by 4,705
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- MonoidWithZeroHomstatement and proof · cited by 704
- MonoidWithZerostatement and proof · cited by 456
- MonoidWithZeroHom.valueMonoidstatement · cited by 10
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