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Theorems · Definition · order theory

Nucleus.toClosureOperator

{X : Type u_1} → [inst : SemilatticeInf X] → Nucleus X → ClosureOperator X

Every nucleus is a ClosureOperator.

Defined in
Mathlib.Order.Nucleus
Cited by
3 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemilatticeInf
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Around this declaration

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

Nucleus.le_apply · cited by 5Nucleus.le_applyNucleus.monotone · cited by 3Nucleus.monotoneNucleus.idempotent · cited by 3Nucleus.idempotentDFunLike.coe · cited by 62936DFunLike.coeSemilatticeInf · cited by 634SemilatticeInfClosureOperator · cited by 371ClosureOperatorNucleus · cited by 41NucleusClosureOperator.mk' · cited by 2ClosureOperator.mk'Nucleus.idempotent' · cited by 1Nucleus.idempotent'Nucleus.le_apply' · cited by 0Nucleus.le_apply'Nucleus.toClosureOperatorCITED BYCITES

Cites7

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.