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Theorems · Definition · order theory

Order.Ideal.toLowerSet

{P : Type u_2} → [inst : LE P] → Order.Ideal P → LowerSet P
Defined in
Mathlib.Order.Ideal
Cited by
9 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
LE
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Around this declaration

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

Order.Ideal.lower · cited by 11Ideal.lowerOrder.Ideal.nonempty' · cited by 2Ideal.nonempty'Order.Ideal.toLowerSet_injective · cited by 1Ideal.toLowerSet_injectiveOrder.Ideal.directed' · cited by 1Ideal.directed'Order.Ideal.coe_sInf · cited by 1Ideal.coe_sInfOrder.Ideal.coe_toLowerSet · cited by 0Ideal.coe_toLowerSetOrder.Ideal.top_toLowerSet · cited by 0Ideal.top_toLowerSetOrder.Ideal.carrier_eq_coe · cited by 0Ideal.carrier_eq_coeOrder.Ideal.principal_toLowerSet · cited by 0Ideal.principal_toLowerSetLowerSet · cited by 230LowerSetOrder.Ideal · cited by 102Order.IdealIdeal.toLowerSetCITED BYCITES

Cites2

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

Cited by9

Results whose statement or proof uses this declaration.