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Theorems · Theorem · order theory

WithBot.preimage_coe_Ici

∀ {α : Type u_1} [inst : Preorder α] {a : α}, WithBot.some ⁻¹' Set.Ici ↑a = Set.Ici a
Defined in
Mathlib.Order.Interval.Set.WithBotTop
Cited by
4 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

EReal.preimage_coe_Ici · cited by 3EReal.preimage_coe_IciWithBot.preimage_coe_Ico · cited by 1WithBot.preimage_coe_IcoWithBot.image_coe_Ici · cited by 1WithBot.image_coe_IciWithBot.preimage_coe_Icc · cited by 1WithBot.preimage_coe_IccSet · cited by 53352SetPreorder · cited by 7952PreorderSet.preimage · cited by 4946Set.preimageSet.ext · cited by 2266Set.extWithBot · cited by 1498WithBotSet.Ici · cited by 1070Set.IciWithBot.some · cited by 541WithBot.someWithBot.coe_le_coe · cited by 76WithBot.coe_le_coeWithBot.preimage_coe_IciCITED 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.