Theorems · Theorem · order theory
LTSeries.exists_relSeries_covBy
∀ {α : Type u_3} [inst : PartialOrder α] [WellFoundedLT α] [WellFoundedGT α] (s : LTSeries α),
∃ t i, t.toFun ∘ ⇑i = s.toFun ∧ i 0 = 0 ∧ i (Fin.last s.length) = Fin.last t.lengthAny LTSeries can be refined to a CovBy-RelSeries
in a bidirectionally well-founded order.
- Defined in
- Mathlib.Order.RelSeries
- Cited by
- 1 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredstatement and proof · cited by 6,101
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- Function.Embeddingstatement and proof · cited by 988
- WellFoundedLTstatement and proof · cited by 491
- CovBystatement and proof · cited by 290
- Equiv.reflproof · cited by 274
- Equiv.toEmbeddingproof · cited by 254
- RelSeries.lengthstatement and proof · cited by 195
- RelSeriesstatement and proof · cited by 129
Cited by1
Results whose statement or proof uses this declaration.
- LTSeries.exists_relSeries_covBy_and_head_eq_bot_and_last_eq_botproof · cited by 1