Theorems · Theorem · order theory
not_isMax_iff
∀ {α : Type u_1} [inst : Preorder α] {a : α}, ¬IsMax a ↔ ∃ b, a < b- Defined in
- Mathlib.Order.Max
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsMaxstatement · cited by 372
- lt_iff_le_not_geproof · cited by 35
Cited by29
Results whose statement or proof uses this declaration.
- not_isMaxproof · cited by 46
- isTop_or_exists_gtproof · cited by 4
- exists_covBy_of_wellFoundedLTproof · cited by 2
- Order.not_isMax_zeroproof · cited by 2
- exists_Icc_mem_subset_of_mem_nhdsGEproof · cited by 2
- IsMax.of_disjoint_nhds_Ioiproof · cited by 2
- PredOrder.accPt_principalproof · cited by 2
- StrictMono.isMax_of_applyproof · cited by 2
- PredOrder.isOpen_singleton_iffproof · cited by 2
- CategoryTheory.Functor.WellOrderInductionData.Extension.mk.injstatement and proof · cited by 1
- CategoryTheory.Functor.WellOrderInductionData.Extension.mk.noConfusionstatement and proof · cited by 1
- WithBot.isPredLimit_iffproof · cited by 1