Theorems · Theorem · order theory

Set.preimage_mul_const_Ico

∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] (a b c : α),
  (fun x => x * a) ⁻¹' Set.Ico b c = Set.Ico (b / a) (c / a)

Defined in

Mathlib.Algebra.Order.Group.Pointwise.Interval

Cited by

3 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupPartialOrderIsOrderedMonoid