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Theorems · Theorem · order theory

isLowerSet_Iic

∀ {α : Type u_1} [inst : Preorder α] (a : α), IsLowerSet (Set.Iic a)
Defined in
Mathlib.Order.UpperLower.Basic
Cited by
8 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
Preorder
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Around this declaration

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

LowerSet.Iic · cited by 37LowerSet.IicRelation.fibration_iff_isLowerSet_image_Iic · cited by 4Relation.fibration_iff_is…Relation.fibration_iff_image_Iic · cited by 2Relation.fibration_iff_im…Relation.fibration_iff_isLowerSet_image · cited by 2Relation.fibration_iff_is…Order.IsNormal.continuous · cited by 1IsNormal.continuousInverseSystem.globalEquiv_naturality · cited by 0InverseSystem.globalEquiv…dirSupInaccOn_Iic · cited by 0dirSupInaccOn_IicdirSupInacc_Iic · cited by 0dirSupInacc_Iicnot_bddBelow_Iic · cited by 0not_bddBelow_IicPreorder · cited by 7952PreorderSet.Iic · cited by 1111Set.Iicle_trans · cited by 985le_transIsLowerSet · cited by 167IsLowerSetisLowerSet_IicCITED BYCITES

Cites4

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.