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Theorems · Theorem · order theory

ClosureOperator.ext_isClosed

∀ {α : Type u_1} [inst : PartialOrder α] (c₁ c₂ : ClosureOperator α),
  (∀ (x : α), c₁.IsClosed x ↔ c₂.IsClosed x) → c₁ = c₂
Defined in
Mathlib.Order.Closure
Cited by
0 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
PartialOrder
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DFunLike.coe · cited by 62936DFunLike.coePartialOrder · cited by 6410PartialOrderSet.ofPred · cited by 6101Set.ofPredClosureOperator · cited by 371ClosureOperatorIsGLB · cited by 213IsGLBClosureOperator.IsClosed · cited by 38ClosureOperator.IsClosedIsGLB.unique · cited by 13IsGLB.uniqueClosureOperator.ext · cited by 4ClosureOperator.extClosureOperator.closure_isGLB · cited by 1ClosureOperator.closure_i…ClosureOperator.ext_isClosedCITED BYCITES

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