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Theorems · Theorem · order theory

OrderHomClass.monotone

∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : FunLike F α β]
  [OrderHomClass F α β] (f : F), Monotone ⇑f
Defined in
Mathlib.Order.Hom.Basic
Cited by
5 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
PreorderPreorderFunLikeOrderHomClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OrderHomClass.toOrderHom · cited by 44OrderHomClass.toOrderHomOrderEmbedding.monotone · cited by 26OrderEmbedding.monotoneOrderMonoidHomClass.toOrderAddMonoidHom · cited by 5OrderMonoidHomClass.toOrd…OrderMonoidHomClass.toOrderMonoidHom · cited by 5OrderMonoidHomClass.toOrd…OrderMonoidWithZeroHomClass.toOrderMonoidWithZeroHom · cited by 4OrderMonoidWithZeroHomCla…OrderRingHomClass.toOrderRingHom · cited by 3OrderRingHomClass.toOrder…ArchimedeanClass.orderHom_injective · cited by 1ArchimedeanClass.orderHom…MulArchimedeanClass.map_mk_le · cited by 0MulArchimedeanClass.map_m…ArchimedeanClass.map_mk_le · cited by 0ArchimedeanClass.map_mk_leMulArchimedeanClass.orderHom_injective · cited by 0MulArchimedeanClass.order…DFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderFunLike · cited by 2560FunLikeMonotone · cited by 1397MonotoneOrderHomClass · cited by 16OrderHomClassRelHomClass.map_rel · cited by 10RelHomClass.map_relOrderHomClass.monotoneCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by10

Results whose statement or proof uses this declaration.