Theorems · Definition · order theory
LocallyFiniteOrder.orderAddMonoidHom
(G : Type u_2) → [inst : AddCommGroup G] → [inst_1 : LinearOrder G] → [IsOrderedAddMonoid G] → [LocallyFiniteOrder G] → G →+o ℤ
The canonical embedding (as an ordered monoid hom) from a linearly ordered cancellative
group into ℤ. This is either surjective or zero.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 74 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.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- AddMonoidHomproof · cited by 3,230
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- LocallyFiniteOrderstatement and proof · cited by 658
- OrderAddMonoidHomstatement · cited by 80
- LocallyFiniteOrder.addMonoidHomproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- LocallyFiniteOrder.orderMonoidHomproof · cited by 4
- LocallyFiniteOrder.orderAddMonoidHom_strictMonostatement and proof · cited by 3
- LocallyFiniteOrder.orderAddMonoidEquivproof · cited by 1
- LocallyFiniteOrder.orderAddMonoidHom_applystatement · cited by 0
- LocallyFiniteOrder.orderAddMonoidHom_bijectivestatement and proof · cited by 0
- LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHomstatement · cited by 0
- LocallyFiniteOrder.orderAddMonoidHom.congr_simpstatement and proof · cited by 0