Theorems · Definition · order theory
OrderIso.withZeroUnits
{α : Type u_1} → [inst : LinearOrderedCommGroupWithZero α] → WithZero αˣ ≃o αGiven any linearly ordered commutative group with zero α, this is the order isomorphism
between WithZero αˣ with α.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 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.
- Unitsstatement and proof · cited by 2,804
- MulEquivproof · cited by 1,142
- OrderIsostatement · cited by 874
- WithZerostatement and proof · cited by 586
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MulEquiv.toEquivproof · cited by 126
- WithZero.withZeroUnitsEquivproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- MonoidWithZeroHom.ValueGroup₀.embedding_strictMonoproof · cited by 12
- OrderIso.withZeroUnits_applystatement and proof · cited by 1
- WithZero.withZeroUnitsEquiv_symm_strictMonoproof · cited by 0
- OrderIso.withZeroUnits_symm_applystatement and proof · cited by 0