proposition: Lemma inv_lfun_def f : (f \o f^-1 \o f)%VF = f.
proof: Proof. apply/lfunP=> u; do !rewrite lfunE /=; rewrite unlock /= !r2vK. by rewrite mulmxKpV ?submxMl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)