∀ {𝕜 : Type u_1} [inst : AddCommGroup 𝕜] [inst_1 : LinearOrder 𝕜] [inst_2 : IsOrderedAddMonoid 𝕜] (p a : 𝕜)
  [hp : Fact (0 < p)] (a_1 b : ↑(Set.Icc a (a + p))),
  AddCircle.EndpointIdent p a a_1 b → (fun x => ↑↑x) a_1 = (fun x => ↑↑x) b