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Theorems · Theorem · order theory

LowerAdjoint.monotone

∀ {α : Type u_1} {β : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] {u : β → α} (l : LowerAdjoint u),
  Monotone (u ∘ l.toFun)
Defined in
Mathlib.Order.Closure
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

FirstOrder.Language.Substructure.closure_mono · cited by 0Substructure.closure_monoPreorder · cited by 7952PreorderMonotone · cited by 1397MonotoneLowerAdjoint.toFun · cited by 105LowerAdjoint.toFunGaloisConnection.monotone_l · cited by 76GaloisConnection.monotone…Monotone.comp · cited by 67Monotone.compGaloisConnection.monotone_u · cited by 53GaloisConnection.monotone…LowerAdjoint · cited by 38LowerAdjointLowerAdjoint.gc · cited by 3LowerAdjoint.gcLowerAdjoint.monotoneCITED BYCITES

Cites8

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Cited by1

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