proposition: Lemma skew_field_module_dimS A M : (A * M <= M)%VS -> \dim A %| \dim M.
proof: Proof. case/skew_field_module_semisimple=> X [<- /directvP-> nzX] /=. rewrite big_seq prime.dvdn_sum // => x /(memPn nzX)nz_x. by rewrite dim_cosetv_unit ?fieldT. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype div tuple finfun bigop ssralg) mathcomp(finalg zmodp matrix vector poly)