Local Notation sr modV := (submod_repr modV).

Lemma mxtrace_component U (simU : mxsimple rG U) :
let V := component_mx rG U in
let modV := component_mx_module rG U in let modU := mxsimple_module simU in
{in G, forall x, \tr (sr modV x) = \tr (sr modU x) *+ (\rank V %/ \rank U)}.