Theorems · Definition · order theory
Interval.length
{α : Type u_2} → [AddCommGroup α] → [inst : PartialOrder α] → Interval α → αThe length of an interval is its first component minus its second component. This measures the accuracy of the approximation by an interval.
- Defined in
- Mathlib.Algebra.Order.Interval.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddCommGroupPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- NonemptyIntervalproof · cited by 139
- Intervalstatement and proof · cited by 76
- NonemptyInterval.lengthproof · cited by 7
Cited by8
Results whose statement or proof uses this declaration.
- Interval.length_add_lestatement and proof · cited by 2
- Interval.length_negstatement and proof · cited by 1
- Interval.length_purestatement · cited by 1
- Interval.length_zerostatement · cited by 1
- Interval.length_botstatement · cited by 0
- Interval.length_nonnegstatement and proof · cited by 0
- Interval.length_sub_lestatement and proof · cited by 0
- Interval.length_sum_lestatement and proof · cited by 0