Theorems · Theorem · order theory
RelSeries.subsingleton_of_length_eq_zero
∀ {α : Type u_1} {r : SetRel α α} {s : RelSeries r}, s.length = 0 → {x | x ∈ s}.Subsingleton- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.ofPredstatement and proof · cited by 6,101
- zero_addproof · cited by 2,366
- SetRelstatement and proof · cited by 581
- Equiv.injectiveproof · cited by 464
- Set.Subsingletonstatement · cited by 276
- RelSeries.lengthstatement and proof · cited by 195
- RelSeriesstatement and proof · cited by 129
- RelSeries.toFunproof · cited by 114
- finCongrproof · cited by 78
Cited by3
Results whose statement or proof uses this declaration.
- RelSeries.length_ne_zero_of_nontrivialproof · cited by 2
- CompositionSeries.exists_last_eq_snoc_equivalentproof · cited by 1
- CompositionSeries.eq_of_head_eq_head_of_last_eq_last_of_length_eq_zeroproof · cited by 1