Mathlib Map

Theorems · Theorem · order theory

RelSeries.rel_of_lt

∀ {α : Type u_1} {r : SetRel α α} [r.IsTrans] (x : RelSeries r) {i j : Fin (x.length + 1)},
  i < j → (x.toFun i, x.toFun j) ∈ r
Defined in
Mathlib.Order.RelSeries
Cited by
3 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SetRel.IsTrans
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LTSeries.strictMono · cited by 7LTSeries.strictMonoOrder.one_lt_height_iff · cited by 0Order.one_lt_height_iffRelSeries.rel_or_eq_of_le · cited by 0RelSeries.rel_or_eq_of_leSetRel · cited by 581SetRelRelSeries.length · cited by 195RelSeries.lengthRelSeries · cited by 129RelSeriesRelSeries.toFun · cited by 114RelSeries.toFunSetRel.IsTrans · cited by 21SetRel.IsTransRelSeries.step · cited by 18RelSeries.stepFin.liftFun_iff_succ · cited by 6Fin.liftFun_iff_succRelSeries.rel_of_ltCITED BYCITES

Cites7

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

Cited by3

Results whose statement or proof uses this declaration.