Theorems · Theorem · order theory

toIocDiv_eq_of_sub_zsmul_mem_Ioc

∀ {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}, b - n • p ∈ Set.Ioc a (a + p) → toIocDiv hp a b = n

Alias of the reverse direction of toIocDiv_eq_iff.

Defined in

Mathlib.Algebra.Order.ToIntervalMod

Cited by

8 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedean