Theorems · Theorem · convex and discrete geometry

Monotone.quasiconvexOn

∀ {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 : LinearOrder E] [IsOrderedAddMonoid E] [inst_5 : PartialOrder β] [inst_6 : Module 𝕜 E] [PosSMulMono 𝕜 E]
  {f : E → β}, Monotone f → QuasiconvexOn 𝕜 Set.univ f

Defined in: Mathlib.Analysis.Convex.Quasiconvex
Cited by: 1 results in Mathlib
Foundations: Depth 21 from the axioms · uses propext, Quot.sound
Assumes: Semiring PartialOrder AddCommMonoid LinearOrder IsOrderedAddMonoid PartialOrder Module PosSMulMono

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Cites13

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

Modulestatement and proof · cited by 20,661
Semiringstatement and proof · cited by 13,802
AddCommMonoidstatement and proof · cited by 12,281
LinearOrderstatement and proof · cited by 8,572
PartialOrderstatement and proof · cited by 6,410
Set.univstatement and proof · cited by 3,945
IsOrderedAddMonoidstatement and proof · cited by 1,659
Monotonestatement and proof · cited by 1,397
PosSMulMonostatement and proof · cited by 188
convex_univproof · cited by 53
Monotone.monotoneOnproof · cited by 43
QuasiconvexOnstatement · cited by 25

Cited by1

Results whose statement or proof uses this declaration.

Monotone.quasilinearOnproof · cited by 0