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Theorems · Theorem · order theory

NonemptyInterval.length_pure

∀ {α : Type u_2} [inst : AddCommGroup α] [inst_1 : PartialOrder α] (a : α), (NonemptyInterval.pure a).length = 0
Defined in
Mathlib.Algebra.Order.Interval.Basic
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext
Assumes
AddCommGroupPartialOrder
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Around this declaration

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

NonemptyInterval.length_zero · cited by 1NonemptyInterval.length_z…Interval.length_pure · cited by 1Interval.length_pureAddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrdersub_self · cited by 996sub_selfNonemptyInterval.toProd · cited by 62NonemptyInterval.toProdNonemptyInterval.pure · cited by 28NonemptyInterval.pureNonemptyInterval.length · cited by 7NonemptyInterval.lengthNonemptyInterval.length_pureCITED 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.