Mathlib Map

Theorems · Theorem · order theory

Set.image_const_mul_Iio

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

Around this declaration

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

Set · cited by 53352SetPartialOrder · cited by 6410PartialOrderSet.image · cited by 5609Set.imageSet.preimage · cited by 4946Set.preimagemul_comm · cited by 2262mul_commSet.Iio · cited by 1166Set.IioCommGroup · cited by 990CommGroupIsOrderedMonoid · cited by 577IsOrderedMonoiddiv_inv_eq_mul · cited by 53div_inv_eq_mulSet.image_mul_left · cited by 21Set.image_mul_leftSet.preimage_mul_const_Iio · cited by 9Set.preimage_mul_const_IioSet.image_const_mul_IioCITED BYCITES

Cites11

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

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.