Theorems · Theorem · order theory

Set.preimage_add_const_Iio

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a b : α),
  (fun x => x + a) ⁻¹' Set.Iio b = Set.Iio (b - a)

Defined in

Mathlib.Algebra.Order.Group.Pointwise.Interval

Cited by

9 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupPartialOrderIsOrderedAddMonoid