Theorems · Theorem · order theory
Function.argminOn_mem
∀ {α : Type u_1} {β : Type u_2} (f : α → β) [inst : LT β] [inst_1 : WellFoundedLT β] (s : Set α) (hs : s.Nonempty),
Function.argminOn f s hs ∈ s- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LTWellFoundedLT
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.
- Setstatement and proof · cited by 53,352
- Set.Nonemptystatement and proof · cited by 2,627
- WellFoundedLTstatement and proof · cited by 491
- WellFounded.min_memproof · cited by 23
- Function.argminOnstatement · cited by 8
Cited by7
Results whose statement or proof uses this declaration.
- isLeast_csInfproof · cited by 4
- Caratheodory.mem_minCardFinsetOfMemConvexHullproof · cited by 3
- Caratheodory.minCardFinsetOfMemConvexHull_subseteqproof · cited by 2
- exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_powproof · cited by 2
- sInf_eq_argmin_onproof · cited by 1
- Function.isMinimalFor_argminOnproof · cited by 0