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Theorems · Theorem · order theory

Set.Subsingleton.equitableOn

∀ {α : Type u_1} {β : Type u_2} [inst : Semiring β] [inst_1 : PartialOrder β] [IsOrderedRing β] {s : Set α},
  s.Subsingleton → ∀ (f : α → β), s.EquitableOn f
Defined in
Mathlib.Data.Set.Equitable
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
SemiringPartialOrderIsOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.equitableOn_singleton · cited by 1Set.equitableOn_singletonSet.Subsingleton.isEquipartition · cited by 1Subsingleton.isEquipartit…Set · cited by 53352SetSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsOrderedRing · cited by 777IsOrderedRingzero_le_one · cited by 316zero_le_oneSet.Subsingleton · cited by 276Set.Subsingletonle_add_of_nonneg_right · cited by 69le_add_of_nonneg_rightSet.EquitableOn · cited by 12Set.EquitableOnSubsingleton.equitableOnCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.