Theorems · Theorem · order theory
RelSeries.last_snoc
∀ {α : Type u_1} {r : SetRel α α} (p : RelSeries r) (newLast : α) (rel : (p.last, newLast) ∈ r),
(p.snoc newLast rel).last = newLast- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 10 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.
Cites6
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.snocstatement · cited by 24
- RelSeries.last_appendproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- Order.height_leproof · cited by 7
- Order.height_strictMonoproof · cited by 5
- Order.length_le_heightproof · cited by 5
- Order.height_eq_iSup_lt_heightproof · cited by 3
- CompositionSeries.exists_last_eq_snoc_equivalentproof · cited by 1
- CompositionSeries.Equivalent.snoc_snoc_swapproof · cited by 1
- PrimeSpectrum.exist_ltSeries_mem_one_of_mem_lastproof · cited by 1
- IsNoetherianRing.exists_relSeries_isQuotientEquivQuotientPrimeproof · cited by 1
- Module.exists_ltSeries_support_isMaximal_last_of_ltSeries_supportproof · cited by 1
- LTSeries.exists_relSeries_covBy_and_head_eq_bot_and_last_eq_botproof · cited by 1