Theorems · Theorem · order theory
Monotone.strictMono_of_injective
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : PartialOrder β] {f : α → β},
Monotone f → Function.Injective f → StrictMono f- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- PreorderPartialOrder
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.
- Preorderstatement and proof · cited by 7,952
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.leproof · cited by 2,189
- Monotonestatement and proof · cited by 1,397
- LT.lt.neproof · cited by 872
- StrictMonostatement · cited by 706
- LE.le.lt_of_neproof · cited by 116
Cited by22
Results whose statement or proof uses this declaration.
- Nat.strictMono_castproof · cited by 12
- ringKrullDim_le_of_surjectiveproof · cited by 4
- add_left_strictMono_of_ne_topproof · cited by 3
- List.SortedLE.sortedLT_of_nodupproof · cited by 2
- add_right_strictMono_of_ne_topproof · cited by 2
- Valuation.nonempty_rankOne_iff_mulArchimedeanproof · cited by 1
- TopologicalSpace.IrreducibleCloseds.map_strictMono_of_isInducingproof · cited by 1
- FirstOrder.Language.HomClass.strictMonoproof · cited by 1
- Finset.Colex.toColex_strictMonoproof · cited by 1
- ArchimedeanClass.orderHom_injectiveproof · cited by 1
- Monotone.strictMono_iff_injectiveproof · cited by 1
- Valuation.IsEquiv.mapproof · cited by 1