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Theorems · Theorem · order theory

List.le_of_mem_argmax

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder β] {f : α → β} {l : List α} {a m : α},
  a ∈ l → m ∈ List.argmax f l → f a ≤ f m
Defined in
Mathlib.Data.List.MinMax
Cited by
3 results in Mathlib
Foundations
Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

List.mem_argmax_iff · cited by 1List.mem_argmax_iffSubmodule.exists_isTorsionBy · cited by 1Submodule.exists_isTorsio…List.le_maximum_of_mem · cited by 1List.le_maximum_of_memLinearOrder · cited by 8572LinearOrderle_of_not_gt · cited by 430le_of_not_gtList.argmax · cited by 15List.argmaxList.not_lt_of_mem_argmax · cited by 2List.not_lt_of_mem_argmaxList.le_of_mem_argmaxCITED BYCITES

Cites4

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Cited by3

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