Theorems · Theorem · order theory
exists_covBy_of_wellFoundedLT
∀ {α : Type u_1} [inst : Preorder α] [wf : WellFoundedLT α] ⦃a : α⦄, ¬IsMax a → ∃ a', a ⋖ a'- Defined in
- Mathlib.Order.Cover
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderWellFoundedLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Ioiproof · cited by 1,463
- WellFoundedLTstatement and proof · cited by 491
- IsMaxstatement and proof · cited by 372
- CovBystatement · cited by 290
- IsWellFounded.wfproof · cited by 43
- WellFounded.minproof · cited by 33
- not_isMax_iffproof · cited by 24
- WellFounded.min_memproof · cited by 23
- wellFounded_ltproof · cited by 22
- WellFounded.not_lt_minproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- exists_covBy_seq_of_wellFoundedLT_wellFoundedGTproof · cited by 2
- LocallyFiniteOrder.orderAddMonoidHom_bijectiveproof · cited by 0