proposition: Lemma invC_norm x : x^-1 = `|x| ^- 2 * x^*.
proof: Proof. have [-> | nx_x] := eqVneq x 0; first by rewrite conjC0 mulr0 invr0. by rewrite normCK invfM divfK ?conjC_eq0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)