Fact unitGI_out : {in [predC unitGI], invGI =1 id}.
Definition GI_comUnitRingMixin :=
ComUnitRingMixin mulGIr unitGIP unitGI_out.
Canonical GI_unitRingType := UnitRingType GI GI_comUnitRingMixin.
Canonical GI_comUnitRingType := [comUnitRingType of GI].

(**  ** Question 7: Find the invertible elements of GI  - This is question 1 of the CPGE exercice  - Suggested strategy: sketch the proof on a paper first, don't let Coq divert you from your proofsketch  *)
Lemma unitGIE (x : GI) : (x \in GRing.unit) =
(val x \in 4.-unity_root).