Theorems · Definition · order theory
OrderMonoidIso.withZeroUnits
{α : Type u_6} → [inst : LinearOrderedCommGroupWithZero α] → [DecidablePred fun a => a = 0] → WithZero αˣ ≃*o αAny linearly ordered group with zero is isomorphic to adjoining 0 to the units of itself.
- Defined in
- Mathlib.Algebra.Order.Hom.MonoidWithZero
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsstatement and proof · cited by 2,804
- MulEquivproof · cited by 1,142
- WithZerostatement and proof · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- OrderMonoidIsostatement · cited by 114
- WithZero.withZeroUnitsEquivproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- OrderMonoidIso.withZeroUnits_symm_applystatement and proof · cited by 1
- LocallyFiniteOrder.orderMonoidWithZeroHomproof · cited by 1
- Units.mulArchimedean_iffproof · cited by 1
- OrderMonoidIso.withZeroUnits_applystatement and proof · cited by 0
- LocallyFiniteOrder.orderMonoidWithZeroEquivproof · cited by 0
- LinearOrderedCommGroupWithZero.discrete_or_denselyOrderedproof · cited by 0