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Theorems · Theorem · order theory

Set.image_subtype_val_uIcc

∀ {α : Type u_1} [inst : LinearOrder α] {s : Set α} [s.OrdConnected] (a b : ↑s),
  Subtype.val '' Set.uIcc a b = Set.uIcc ↑a ↑b
Defined in
Mathlib.Order.Interval.Set.OrdConnected
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSet.OrdConnected
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Around this declaration

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

NNReal.image_coe_uIcc · cited by 0NNReal.image_coe_uIccSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Elem · cited by 7166Set.ElemSet.image · cited by 5609Set.imageSet.Icc · cited by 1702Set.IccSet.uIcc · cited by 393Set.uIccSet.OrdConnected · cited by 161Set.OrdConnectedSubtype.mono_coe · cited by 15Subtype.mono_coeMonotone.map_inf · cited by 8Monotone.map_infMonotone.map_sup · cited by 6Monotone.map_supSet.image_subtype_val_Icc · cited by 4Set.image_subtype_val_IccSet.image_subtype_val_uIccCITED BYCITES

Cites11

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Cited by1

Results whose statement or proof uses this declaration.