Mathlib Map

Theorems · Theorem · order theory

isMax_iff_forall_not_lt

∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsMax a ↔ ∀ (b : α), ¬a < b
Defined in
Mathlib.Order.Max
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.Ioi_eq_empty_iff · cited by 3Set.Ioi_eq_empty_iffHahnEmbedding.Partial.exists_domain_eq_top · cited by 1Partial.exists_domain_eq_…Preorder · cited by 7952PreorderIsMax · cited by 372IsMaxof_not_not · cited by 51of_not_notLE.le.lt_of_not_ge · cited by 21le.lt_of_not_geIsMax.not_lt · cited by 8IsMax.not_ltisMax_iff_forall_not_ltCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.