Mathlib Map

Theorems · Definition · order theory

Interval.coe

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

Canonical coercion from nonempty intervals to intervals

Defined in
Mathlib.Order.Interval.Basic
Cited by
28 results in Mathlib
Foundations
Depth 3 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.pure · cited by 15Interval.pureInterval.recBotCoe · cited by 4Interval.recBotCoeInterval.coe_inj · cited by 2Interval.coe_injNonemptyInterval.coe_zero_interval · cited by 1NonemptyInterval.coe_zero…Interval.coe_inf · cited by 1Interval.coe_infInterval.coe_sInf · cited by 1Interval.coe_sInfNonemptyInterval.coe_add_interval · cited by 1NonemptyInterval.coe_add_…NonemptyInterval.coe_eq_pure · cited by 1NonemptyInterval.coe_eq_p…NonemptyInterval.coe_mul_interval · cited by 1NonemptyInterval.coe_mul_…Interval.coe_injective · cited by 1Interval.coe_injectiveNonemptyInterval.coe_one_interval · cited by 1NonemptyInterval.coe_one_…NonemptyInterval.coe_pure_interval · cited by 1NonemptyInterval.coe_pure…Interval.dual_map · cited by 0Interval.dual_mapInterval.exists · cited by 0Interval.existsInterval.forall · cited by 0Interval.forallWithBot.some · cited by 541WithBot.someNonemptyInterval · cited by 139NonemptyIntervalInterval · cited by 76IntervalInterval.coeCITED BYCITES

Cites3

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

Cited by30

Results whose statement or proof uses this declaration.