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Theorems · Theorem · order theory

ClosureOperator.closure_top

∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderTop α] (c : ClosureOperator α), c ⊤ = ⊤
Defined in
Mathlib.Order.Closure
Cited by
4 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
PartialOrderOrderTop
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Around this declaration

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

convexHull_univ · cited by 3convexHull_univClosureOperator.isClosed_top · cited by 0ClosureOperator.isClosed_…absConvexHull_univ · cited by 0absConvexHull_univLowerAdjoint.closure_top · cited by 0LowerAdjoint.closure_topDFunLike.coe · cited by 62936DFunLike.coeTop.top · cited by 9680Top.topPartialOrder · cited by 6410PartialOrderLE.le.antisymm · cited by 507le.antisymmOrderTop · cited by 493OrderTople_top · cited by 411le_topClosureOperator · cited by 371ClosureOperatorClosureOperator.le_closure · cited by 19ClosureOperator.le_closureClosureOperator.closure_topCITED BYCITES

Cites8

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

Cited by4

Results whose statement or proof uses this declaration.