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Theorems · Theorem · order theory

ClosureOperator.isClosed_closure

∀ {α : Type u_1} [inst : Preorder α] (c : ClosureOperator α) (x : α), c.IsClosed (c x)
Defined in
Mathlib.Order.Closure
Cited by
15 results in Mathlib
Foundations
Depth 15 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.

convex_convexHull · cited by 25convex_convexHullsupClosed_supClosure · cited by 8supClosed_supClosurecountableInfClosed_countableInfClosure · cited by 5countableInfClosed_counta…infClosed_infClosure · cited by 5infClosed_infClosureisSublattice_latticeClosure · cited by 5isSublattice_latticeClosu…countableSupClosed_countableSupClosure · cited by 5countableSupClosed_counta…absConvex_absConvexHull · cited by 4absConvex_absConvexHullClosureOperator.setOfPred_isClosed_eq_range_closure · cited by 2ClosureOperator.setOfPred…isClosed_closedAbsConvexHull · cited by 2isClosed_closedAbsConvexH…isClosed_closedConvexHull · cited by 2isClosed_closedConvexHullConvexity.IsConvexSet.convexHull · cited by 1IsConvexSet.convexHullClosureOperator.toCloseds · cited by 1ClosureOperator.toClosedsClosureOperator.closure_isGLB · cited by 1ClosureOperator.closure_i…absConvex_convexClosedHull · cited by 1absConvex_convexClosedHullconvex_closedConvexHull · cited by 1convex_closedConvexHullDFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderClosureOperator · cited by 371ClosureOperatorClosureOperator.IsClosed · cited by 38ClosureOperator.IsClosedClosureOperator.isClosed_iff · cited by 14ClosureOperator.isClosed_…ClosureOperator.idempotent · cited by 12ClosureOperator.idempotentClosureOperator.isClosed_clos…CITED BYCITES

Cites6

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

Cited by16

Results whose statement or proof uses this declaration.