Theorems · Theorem · order theory
isBot_or_exists_lt
∀ {α : Type u_1} [inst : Preorder α] [IsCodirectedOrder α] (a : α), IsBot a ∨ ∃ b, b < a- Defined in
- Mathlib.Order.Directed
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsCodirectedOrder
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.
- Preorderstatement and proof · cited by 7,952
- IsMinproof · cited by 277
- emproof · cited by 115
- IsCodirectedOrderstatement and proof · cited by 95
- IsBotstatement · cited by 77
- not_isMin_iffproof · cited by 18
- IsMin.isBotproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Filter.IsCobounded.frequently_geproof · cited by 3
- Filter.IsCobounded.of_frequently_geproof · cited by 3
- exists_lt_of_directed_geproof · cited by 1