fact: Definition prodv := locked_with prodv_key (fun U V => <<allpairs *%R (vbasis U) (vbasis V)>>%VS).
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)