Theorems · Theorem · order theory
IsMax.isTop
∀ {α : Type u_1} [inst : Preorder α] {a : α} [IsDirectedOrder α], IsMax a → IsTop a- Defined in
- Mathlib.Order.Directed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- PreorderIsDirectedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- LE.le.transproof · cited by 3,151
- IsMaxstatement and proof · cited by 372
- IsDirectedOrderstatement and proof · cited by 316
- IsTopstatement · cited by 77
- exists_ge_geproof · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- isTop_or_exists_gtproof · cited by 4
- IsMax.not_isMinproof · cited by 2
- isTop_iff_isMaxproof · cited by 1
- Flag.isMax_coeproof · cited by 0