Theorems · Theorem · order theory
RelSeries.length_eq_zero
∀ {α : Type u_1} {r : SetRel α α} {s : RelSeries r} [r.IsIrrefl], s.length = 0 ↔ {x | x ∈ s}.Subsingleton- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SetRel.IsIrrefl
Around this declaration
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Cites9
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
- Set.Subsingletonstatement and proof · cited by 276
- RelSeries.lengthstatement · cited by 195
- RelSeriesstatement and proof · cited by 129
- not_ne_iffproof · cited by 30
- Set.not_nontrivial_iffproof · cited by 13
- SetRel.IsIrreflstatement and proof · cited by 4
- RelSeries.length_ne_zeroproof · cited by 2
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