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Theorems · Theorem · order theory

WithTop.preimage_coe_Iio

∀ {α : Type u_1} [inst : Preorder α] {a : α}, WithTop.some ⁻¹' Set.Iio ↑a = Set.Iio a
Defined in
Mathlib.Order.Interval.Set.WithBotTop
Cited by
4 results in Mathlib
Foundations
Depth 17 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.

WithTop.image_coe_Iio · cited by 4WithTop.image_coe_IioEReal.preimage_coe_Iio · cited by 3EReal.preimage_coe_IioWithTop.preimage_coe_Ico · cited by 1WithTop.preimage_coe_IcoWithTop.preimage_coe_Ioo · cited by 1WithTop.preimage_coe_IooSet · cited by 53352SetPreorder · cited by 7952PreorderSet.preimage · cited by 4946Set.preimageWithTop · cited by 3754WithTopSet.ext · cited by 2266Set.extSet.Iio · cited by 1166Set.IioWithTop.some · cited by 1128WithTop.someWithTop.coe_lt_coe · cited by 47WithTop.coe_lt_coeWithTop.preimage_coe_IioCITED BYCITES

Cites8

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

Cited by4

Results whose statement or proof uses this declaration.