Theorems · Theorem · order theory
ArchimedeanClass.orderHom_injective
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {N : Type u_2}
[inst_3 : AddCommGroup N] [inst_4 : LinearOrder N] [inst_5 : IsOrderedAddMonoid N] {f : M →+o N},
Function.Injective ⇑f → Function.Injective ⇑(ArchimedeanClass.orderHom f)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- OrderHomstatement · cited by 934
- ArchimedeanClassstatement and proof · cited by 247
- StrictMono.le_iff_leproof · cited by 104
- OrderAddMonoidHomstatement and proof · cited by 80
- map_nsmulproof · cited by 41
- Monotone.strictMono_of_injectiveproof · cited by 22
- ArchimedeanClass.orderHomstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- HahnEmbedding.Partial.archimedeanClassMk_eq_iffproof · cited by 1