Theorems · Theorem · order theory
RelSeries.head_snoc
∀ {α : Type u_1} {r : SetRel α α} (p : RelSeries r) (newLast : α) (rel : (p.last, newLast) ∈ r),
(p.snoc newLast rel).head = p.head- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.headstatement and proof · cited by 89
- RelSeries.singletonproof · cited by 25
- RelSeries.snocstatement · cited by 24
- RelSeries.head_appendproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- CompositionSeries.exists_last_eq_snoc_equivalentproof · cited by 1
- IsNoetherianRing.exists_relSeries_isQuotientEquivQuotientPrimeproof · cited by 1
- LTSeries.exists_relSeries_covBy_and_head_eq_bot_and_last_eq_botproof · cited by 1
- PrimeSpectrum.exist_ltSeries_mem_one_of_mem_lastproof · cited by 1