Theorems · Theorem · order theory
RelSeries.length_pos_of_nontrivial
∀ {α : Type u_1} {r : SetRel α α} {s : RelSeries r}, {x | x ∈ s}.Nontrivial → 0 < s.length- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- SetRelstatement and proof · cited by 581
- RelSeries.lengthstatement · cited by 195
- Set.Nontrivialstatement and proof · cited by 145
- RelSeriesstatement and proof · cited by 129
- RelSeries.length_ne_zero_of_nontrivialproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CompositionSeries.mem_eraseLast_of_ne_of_memproof · cited by 1