Mathlib Map

Theorems · Theorem · order theory

NonemptyInterval.fst_le_snd

∀ {α : Type u_6} [inst : LE α] (self : NonemptyInterval α), self.toProd.1 ≤ self.toProd.2

The starting point of an interval is smaller than the endpoint.

Defined in
Mathlib.Order.Interval.Basic
Cited by
6 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.

NonemptyInterval.dual · cited by 7NonemptyInterval.dualNonemptyInterval.mul_eq_one_iff · cited by 1NonemptyInterval.mul_eq_o…Interval.coe_inf · cited by 1Interval.coe_infNonemptyInterval.add_eq_zero_iff · cited by 1NonemptyInterval.add_eq_z…NonemptyInterval.length_nonneg · cited by 1NonemptyInterval.length_n…NonemptyInterval.coe_nonempty · cited by 0NonemptyInterval.coe_none…Interval.inf_coe · cited by 0Interval.inf_coeNonemptyInterval · cited by 139NonemptyIntervalNonemptyInterval.toProd · cited by 62NonemptyInterval.toProdNonemptyInterval.fst_le_sndCITED BYCITES

Cites2

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

Cited by7

Results whose statement or proof uses this declaration.