Theorems · Definition · order theory
RelSeries.snoc
{α : Type u_1} → {r : SetRel α α} → (p : RelSeries r) → (newLast : α) → (p.last, newLast) ∈ r → RelSeries rGiven a series a₀ -r→ a₁ -r→ ... -r→ aₙ and an a such that aₙ -r→ a holds, there is
a series of length n+1: a₀ -r→ a₁ -r→ ... -r→ aₙ -r→ a.
- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetRelstatement and proof · cited by 581
- RelSeriesstatement and proof · cited by 129
- RelSeries.laststatement and proof · cited by 114
- RelSeries.singletonproof · cited by 25
- RelSeries.appendproof · cited by 11
Cited by25
Results whose statement or proof uses this declaration.
- RelSeries.last_snocstatement · cited by 10
- RelSeries.snoc_lengthstatement and proof · cited by 8
- Order.height_leproof · cited by 7
- Order.height_strictMonoproof · cited by 5
- Order.length_le_heightproof · cited by 5
- RelSeries.head_snocstatement · cited by 4
- Order.height_eq_iSup_lt_heightproof · cited by 3
- RelSeries.snoc_castSuccstatement · cited by 3
- CompositionSeries.eq_snoc_eraseLaststatement · cited by 3
- RelSeries.snoc.congr_simpstatement and proof · cited by 2
- CompositionSeries.Equivalent.snocstatement and proof · cited by 2
- RelSeries.last_snoc'statement · cited by 2