Theorems · Definition · order theory
OrderMonoidIso.unitsWithZero
{α : Type u_6} → [inst : Group α] → [inst_1 : Preorder α] → (WithZero α)ˣ ≃*o αAny ordered group is isomorphic to the units of itself adjoined with 0.
- Defined in
- Mathlib.Algebra.Order.Hom.MonoidWithZero
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Groupstatement and proof · cited by 6,238
- Unitsstatement and proof · cited by 2,804
- MulEquivproof · cited by 1,142
- WithZerostatement and proof · cited by 586
- OrderMonoidIsostatement · cited by 114
- WithZero.unitsWithZeroEquivproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- WithZero.mulArchimedean_iffproof · cited by 0
- OrderMonoidIso.unitsWithZero_applystatement and proof · cited by 0
- OrderMonoidIso.val_inv_unitsWithZero_symm_applystatement and proof · cited by 0
- OrderMonoidIso.val_unitsWithZero_symm_applystatement and proof · cited by 0