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Theorems · Theorem · order theory

Set.image_mul_const_Iio

∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] (a b : α),
  (fun x => x * a) '' Set.Iio b = Set.Iio (b * a)
Defined in
Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommGroupPartialOrderIsOrderedMonoid
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Around this declaration

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

Set.Iio_mul_bij · cited by 0Set.Iio_mul_bijSet · cited by 53352SetPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageSet.Iio · cited by 1166Set.IioCommGroup · cited by 990CommGroupIsOrderedMonoid · cited by 577IsOrderedMonoiddiv_inv_eq_mul · cited by 53div_inv_eq_mulSet.image_mul_right · cited by 24Set.image_mul_rightSet.preimage_mul_const_Iio · cited by 9Set.preimage_mul_const_IioSet.image_mul_const_IioCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.