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Theorems · Definition · order theory

ClosureOperator.toCloseds

{α : Type u_1} → [inst : Preorder α] → (c : ClosureOperator α) → α → c.Closeds

Send an element to a closed element (by taking the closure).

Defined in
Mathlib.Order.Closure
Cited by
1 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ClosureOperator.gi · cited by 1ClosureOperator.giclosureOperator_gi_self · cited by 0closureOperator_gi_selfDFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderClosureOperator · cited by 371ClosureOperatorClosureOperator.isClosed_closure · cited by 15ClosureOperator.isClosed_…ClosureOperator.Closeds · cited by 1ClosureOperator.ClosedsClosureOperator.toClosedsCITED BYCITES

Cites5

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

Cited by2

Results whose statement or proof uses this declaration.