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Theorems · Theorem · order theory

ClosureOperator.closure_isGLB

∀ {α : Type u_1} [inst : Preorder α] {c : ClosureOperator α} (x : α), IsGLB {y | x ≤ y ∧ c.IsClosed y} (c x)
Defined in
Mathlib.Order.Closure
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Quot.sound
Assumes
Preorder
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Around this declaration

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

ClosureOperator.ext_isClosed · cited by 0ClosureOperator.ext_isClo…DFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderSet.ofPred · cited by 6101Set.ofPredClosureOperator · cited by 371ClosureOperatorIsGLB · cited by 213IsGLBlowerBounds · cited by 212lowerBoundsClosureOperator.IsClosed · cited by 38ClosureOperator.IsClosedClosureOperator.le_closure · cited by 19ClosureOperator.le_closureClosureOperator.isClosed_closure · cited by 15ClosureOperator.isClosed_…ClosureOperator.closure_min · cited by 12ClosureOperator.closure_m…ClosureOperator.closure_isGLBCITED BYCITES

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.