Theorems · Theorem · order theory

AddCommGroup.modEq_iff_toIocMod_eq_right

∀ {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}, a ≡ b [PMOD p] ↔ toIocMod hp a b = a + p

Defined in

Mathlib.Algebra.Order.ToIntervalMod

Cited by

2 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedean