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Theorems · Theorem · order theory

Set.uIoo_subset_uIcc_self

∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, Set.uIoo a b ⊆ Set.uIcc a b
Defined in
Mathlib.Order.Interval.Set.UnorderedInterval
Cited by
2 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
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Around this declaration

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

exists_eq_interval_average_of_nullSingletonClass · cited by 2exists_eq_interval_averag…exists_isExtrOn_uIoo_of_tendsto · cited by 1exists_isExtrOn_uIoo_of_t…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.uIcc · cited by 393Set.uIccSet.uIoo · cited by 68Set.uIooSet.uIoo_subset_uIcc_selfCITED BYCITES

Cites4

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.