Mathlib Map

Theorems · Definition · order theory

Interval

(α : Type u_6) → [LE α] → Type u_6

The closed intervals in an order. We represent intervals either as ⊥ or a nonempty interval given by its endpoints fst, snd. To convert intervals to the set of elements between these endpoints, use the coercion Interval α → Set α.

Defined in
Mathlib.Order.Interval.Basic
Cited by
76 results in Mathlib
Foundations
Depth 2 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.coe · cited by 28Interval.coeInterval.pure · cited by 15Interval.pureInterval.length · cited by 8Interval.lengthInterval.dual · cited by 5Interval.dualInterval.map · cited by 4Interval.mapInterval.recBotCoe · cited by 4Interval.recBotCoeInterval.add_bot · cited by 3Interval.add_botInterval.bot_ne_pure · cited by 3Interval.bot_ne_pureInterval.bot_add · cited by 2Interval.bot_addInterval.coeHom · cited by 2Interval.coeHomInterval.coe_inj · cited by 2Interval.coe_injInterval.length_add_le · cited by 2Interval.length_add_leInterval.mul_bot · cited by 2Interval.mul_botInterval.pure_ne_bot · cited by 2Interval.pure_ne_botNonemptyInterval.coe_add_interval · cited by 1NonemptyInterval.coe_add_…WithBot · cited by 1498WithBotNonemptyInterval · cited by 139NonemptyIntervalIntervalCITED BYCITES

Cites2

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

Cited by83

Results whose statement or proof uses this declaration.