Theorems · Theorem · order theory

AddCommGroup.tfae_modEq

∀ {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], ∀ (z : ℤ), b - z • p ∉ Set.Ioo a (a + p), toIcoMod hp a b ≠ toIocMod hp a b,
      toIcoMod hp a b + p = toIocMod hp a b].TFAE

Defined in

Mathlib.Algebra.Order.ToIntervalMod

Cited by

3 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidArchimedean