Theorems · Theorem · order theory
isTop_or_exists_gt
∀ {α : Type u_1} [inst : Preorder α] [IsDirectedOrder α] (a : α), IsTop a ∨ ∃ b, a < b- Defined in
- Mathlib.Order.Directed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsDirectedOrder
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
- IsMaxproof · cited by 372
- IsDirectedOrderstatement and proof · cited by 316
- emproof · cited by 115
- IsTopstatement · cited by 77
- not_isMax_iffproof · cited by 24
- IsMax.isTopproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Filter.IsCobounded.of_frequently_leproof · cited by 3
- Filter.IsCobounded.frequently_leproof · cited by 3
- eventually_le_const_iff_forall_gt_eventually_lt_constproof · cited by 2
- exists_lt_of_directed_leproof · cited by 1