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Theorems · Definition · order theory

NonemptyInterval.toDualProd

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

The injection that induces the order on intervals.

Defined in
Mathlib.Order.Interval.Basic
Cited by
5 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
LE
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

NonemptyInterval.toDualProdHom · cited by 1NonemptyInterval.toDualPr…NonemptyInterval.toDualProd_mono · cited by 1NonemptyInterval.toDualPr…NonemptyInterval.toDualProd_strictMono · cited by 1NonemptyInterval.toDualPr…NonemptyInterval.toDualProdHom_apply · cited by 0NonemptyInterval.toDualPr…NonemptyInterval.toDualProd_apply · cited by 0NonemptyInterval.toDualPr…NonemptyInterval.toDualProd_injective · cited by 0NonemptyInterval.toDualPr…OrderDual · cited by 927OrderDualNonemptyInterval · cited by 139NonemptyIntervalNonemptyInterval.toProd · cited by 62NonemptyInterval.toProdNonemptyInterval.toDualProdCITED BYCITES

Cites3

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

Cited by6

Results whose statement or proof uses this declaration.