Mathlib Map

Theorems · Theorem · order theory

IsMax.eq_of_le

∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, IsMax a → a ≤ b → a = b
Defined in
Mathlib.Order.Max
Cited by
5 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
PartialOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isMax_iff_eq_top · cited by 6isMax_iff_eq_topSet.subsingleton_isTop · cited by 5Set.subsingleton_isTopisTop_iff_eq_top · cited by 3isTop_iff_eq_topLocalSubring.map_maximalIdeal_eq_top_of_isMax · cited by 1LocalSubring.map_maximalI…LocalSubring.mem_of_isMax_of_isIntegral · cited by 1LocalSubring.mem_of_isMax…PartialOrder · cited by 6410PartialOrderLE.le.antisymm · cited by 507le.antisymmIsMax · cited by 372IsMaxIsMax.eq_of_leCITED BYCITES

Cites3

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

Cited by5

Results whose statement or proof uses this declaration.