theorem
  for v being Vector of the ModuleStr of V st a=v holds r*a = r*v
proof
  let v be Vector of (the ModuleStr of V) such that
A1: a=v;
  thus r*a = (the lmult of V).(r,a) by VECTSP_1:def 12
    .= r*v by A1,VECTSP_1:def 12;
end;
