Theorems · Theorem · order theory
exists_covBy_seq_of_wellFoundedLT_wellFoundedGT
∀ (α : Type u_2) [inst : Preorder α] [Nonempty α] [wfl : WellFoundedLT α] [wfg : WellFoundedGT α], ∃ a, IsMin (a 0) ∧ ∃ n, IsMax (a n) ∧ ∀ i < n, a i ⋖ a (i + 1)
- Defined in
- Mathlib.Order.OrderIsoNat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Set.univproof · cited by 3,945
- Set.Nonemptyproof · cited by 2,627
- WellFoundedLTstatement and proof · cited by 491
- Set.mem_univproof · cited by 416
- IsMaxstatement and proof · cited by 372
- CovBystatement and proof · cited by 290
- IsMinstatement · cited by 277
- WellFoundedGTstatement and proof · cited by 114
- IsWellFounded.wfproof · cited by 43
- WellFounded.minproof · cited by 33
- WellFounded.min_memproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- exists_compositionSeries_of_isNoetherian_isArtinianproof · cited by 2
- exists_covBy_seq_of_wellFoundedLT_wellFoundedGT_of_leproof · cited by 1