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Theorems · Theorem · order theory

LowerAdjoint.gc

∀ {α : Type u_1} {β : Type u_4} [inst : Preorder α] [inst_1 : Preorder β] {u : β → α} (l : LowerAdjoint u),
  GaloisConnection l.toFun u
Defined in
Mathlib.Order.Closure
Cited by
3 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LowerAdjoint.le_iff_subset · cited by 2LowerAdjoint.le_iff_subsetLowerAdjoint.le_closure · cited by 2LowerAdjoint.le_closureLowerAdjoint.monotone · cited by 1LowerAdjoint.monotonePreorder · cited by 7952PreorderGaloisConnection · cited by 253GaloisConnectionLowerAdjoint.toFun · cited by 105LowerAdjoint.toFunLowerAdjoint · cited by 38LowerAdjointLowerAdjoint.gc' · cited by 1LowerAdjoint.gc'LowerAdjoint.gcCITED BYCITES

Cites5

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

Cited by3

Results whose statement or proof uses this declaration.