Theorems · Theorem · order theory
List.not_lt_of_mem_argmin
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder β] [inst_1 : DecidableLT β] {f : α → β} {l : List α} {a m : α},
a ∈ l → m ∈ List.argmin f l → ¬f a < f m- Defined in
- Mathlib.Data.List.MinMax
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderDecidableLT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- lt_irreflproof · cited by 190
- List.argminstatement · cited by 13
- gt_transproof · cited by 4
- List.not_of_mem_foldl_argAuxproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- List.le_of_mem_argminproof · cited by 2
- List.not_lt_minimum_of_memproof · cited by 1