Theorems · Theorem · order theory
Function.isMinimalFor_argminOn
∀ {α : Type u_1} {β : Type u_2} (f : α → β) [inst : LinearOrder β] [inst_1 : WellFoundedLT β] (s : Set α)
(hs : s.Nonempty), MinimalFor (fun x => x ∈ s) f (Function.argminOn f s hs)- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderWellFoundedLT
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Nonemptystatement and proof · cited by 2,627
- WellFoundedLTstatement and proof · cited by 491
- MinimalForstatement · cited by 23
- Function.argminOnstatement and proof · cited by 8
- Function.argminOn_memproof · cited by 7
- Function.argminOn_leproof · cited by 5
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