Theorems · Theorem · order theory
StrictMono.injective
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : Preorder β] {f : α → β},
StrictMono f → Function.Injective f- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 94 results in Mathlib
- Foundations
- Depth 16 from the axioms, rests on 50 definitions · uses propext
- Assumes
- LinearOrderPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- StrictMonostatement and proof · cited by 706
- Ordering.Comparesproof · cited by 31
- StrictMono.comparesproof · cited by 1
Cited by95
Results whose statement or proof uses this declaration.
- Real.exp_injectiveproof · cited by 12
- StrictMono.isEmbedding_of_ordConnectedproof · cited by 9
- Cardinal.ord_injectiveproof · cited by 5
- List.SortedLT.nodupproof · cited by 5
- strongRankCondition_iff_succproof · cited by 4
- Real.arctan_injectiveproof · cited by 4
- HahnEmbedding.Partial.orderTop_eq_archimedeanClassMkproof · cited by 3
- StrictMono.orderIsoproof · cited by 3
- Real.sinh_injectiveproof · cited by 3
- Polynomial.card_support_eqproof · cited by 3
- EReal.coe_ennreal_injectiveproof · cited by 3
- zsmul_left_injproof · cited by 3