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Theorems · Theorem · order theory

Set.uIoo_of_gt

∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, b < a → Set.uIoo a b = Set.Ioo b a
Defined in
Mathlib.Order.Interval.Set.UnorderedInterval
Cited by
2 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext
Assumes
LinearOrder
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Around this declaration

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

continuousOn_uIcc_extendFrom_uIoo · cited by 1continuousOn_uIcc_extendF…Set.uIoo_of_not_le · cited by 0Set.uIoo_of_not_leSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderLT.lt.le · cited by 2189lt.leSet.Ioo · cited by 1214Set.IooSet.uIoo · cited by 68Set.uIooSet.uIoo_of_ge · cited by 3Set.uIoo_of_geSet.uIoo_of_gtCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.