Theorems · Theorem · group theory
MonoidWithZeroHom.mem_valueGroup
∀ {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.valueGroup- Defined in
- Mathlib.Algebra.GroupWithZero.Range
- Cited by
- 4 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.
Cites13
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.coeproof · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- Subgroupstatement and proof · cited by 3,593
- 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.valueGroupstatement · cited by 170
- MonoidWithZeroHom.valueMonoidproof · cited by 10
- Subgroup.mem_closureproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Valuation.exists_pow_Uniformizerproof · cited by 3
- MonoidWithZeroHom.mem_valueGroup_iff_of_commproof · cited by 3
- MonoidWithZeroHom.inv_mem_valueGroupproof · cited by 1
- MonoidWithZeroHom.ValueGroup₀.restrict₀_of_ne_zerostatement and proof · cited by 0