Theorems · Theorem · general topology

AddCircle.exists_gcd_eq_one_of_isOfFinAddOrder

∀ {𝕜 : Type u_1} [inst : Field 𝕜] {p : 𝕜} [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] [hp : Fact (0 < p)]
  {u : AddCircle p},
  IsOfFinAddOrder u → ∃ m, m.gcd (addOrderOf u) = 1 ∧ m < addOrderOf u ∧ ↑(↑m / ↑(addOrderOf u) * p) = u

Defined in

Mathlib.Topology.Instances.AddCircle.Defs

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingFact