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Theorems · Definition · order theory

NonemptyInterval.dual

{α : Type u_1} → [inst : LE α] → NonemptyInterval α ≃ NonemptyInterval αᵒᵈ

Turn an interval into an interval in the dual order.

Defined in
Mathlib.Order.Interval.Basic
Cited by
7 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
LE
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Around this declaration

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

Interval.dual · cited by 5Interval.dualNonemptyInterval.coe_dual · cited by 1NonemptyInterval.coe_dualNonemptyInterval.dual_map · cited by 0NonemptyInterval.dual_mapNonemptyInterval.dual_map₂ · cited by 0NonemptyInterval.dual_map₂NonemptyInterval.dual_pure · cited by 0NonemptyInterval.dual_pureNonemptyInterval.dual_top · cited by 0NonemptyInterval.dual_topNonemptyInterval.snd_dual · cited by 0NonemptyInterval.snd_dualNonemptyInterval.fst_dual · cited by 0NonemptyInterval.fst_dualEquiv · cited by 8337EquivOrderDual · cited by 927OrderDualNonemptyInterval · cited by 139NonemptyIntervalNonemptyInterval.toProd · cited by 62NonemptyInterval.toProdNonemptyInterval.fst_le_snd · cited by 6NonemptyInterval.fst_le_s…NonemptyInterval.dualCITED BYCITES

Cites5

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

Cited by8

Results whose statement or proof uses this declaration.