Theorems · Definition · order theory
RelSeries.last
{α : Type u_1} → {r : SetRel α α} → RelSeries r → αEnd of a series, i.e. for a₀ -r→ a₁ -r→ ... -r→ aₙ, its last element is aₙ.
Since a relation series is assumed to be non-empty, this is well defined.
- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 114 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 37 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetRelstatement and proof · cited by 581
- RelSeries.lengthproof · cited by 195
- RelSeriesstatement and proof · cited by 129
- RelSeries.toFunproof · cited by 114
Cited by119
Results whose statement or proof uses this declaration.
- Order.heightproof · cited by 67
- RelSeries.snocstatement and proof · cited by 24
- RelSeries.smashstatement and proof · cited by 15
- RelSeries.appendstatement and proof · cited by 11
- RelSeries.last_snocstatement and proof · cited by 10
- Order.length_le_height_laststatement · cited by 9
- RelSeries.snoc_lengthstatement and proof · cited by 8
- Module.length_ne_top_iffproof · cited by 8
- Order.height_lestatement and proof · cited by 7
- Module.length_eq_add_of_exactproof · cited by 6
- Order.height_top_eq_krullDimproof · cited by 6
- Order.length_le_heightstatement and proof · cited by 5