Theorems · Theorem · convex and discrete geometry

QuasilinearOn.dual

∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : LE β] [inst_4 : SMul 𝕜 E] {s : Set E} {f : E → β},
  QuasilinearOn 𝕜 s f → QuasilinearOn 𝕜 s (⇑OrderDual.toDual ∘ f)

Defined in: Mathlib.Analysis.Convex.Quasiconvex
Cited by: 0 results in Mathlib
Foundations: Depth 16 from the axioms · uses Quot.sound
Assumes: Semiring PartialOrder AddCommMonoid LE SMul

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

DFunLike.coestatement · cited by 62,936
Setstatement and proof · cited by 53,352
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
Equivstatement · cited by 8,337
PartialOrderstatement and proof · cited by 6,410
OrderDualstatement · cited by 927
OrderDual.toDualstatement · cited by 481
QuasilinearOnstatement · cited by 11

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