Theorems · Theorem · order theory

toIcoDiv_eq_iff

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [inst_2 : IsOrderedAddMonoid α] [hα : Archimedean α]
  {p : α} (hp : 0 < p) {a b : α} {n : ℤ}, toIcoDiv hp a b = n ↔ b - n • p ∈ Set.Ico a (a + p)

Defined in

Mathlib.Algebra.Order.ToIntervalMod

Cited by

3 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedean