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Theorems · Theorem · order theory

Set.image_mul_left_Ioo

∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] {a : G₀},
  0 < a → ∀ (b c : G₀), (fun x => a * x) '' Set.Ioo b c = Set.Ioo (a * b) (a * c)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupWithZeroPartialOrderPosMulReflectLT
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Around this declaration

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Set.image_affine_Ioo · cited by 1Set.image_affine_IooSet · cited by 53352SetPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageSet.Ioo · cited by 1214Set.IooGroupWithZero · cited by 691GroupWithZeroPosMulReflectLT · cited by 278PosMulReflectLTOrderIso.mulLeft₀ · cited by 25OrderIso.mulLeft₀OrderIso.image_Ioo · cited by 3OrderIso.image_IooSet.image_mul_left_IooCITED BYCITES

Cites8

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Cited by1

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