theorem
  for V being ComplexLinearSpace, v being VECTOR of V, L being
C_Linear_Combination of {v} st L is convex holds ( ex r being Real st r = L.v &
  r = 1 ) & Sum L = L.v * v
proof
  let V be ComplexLinearSpace;
  let v be VECTOR of V;
  let L be C_Linear_Combination of {v};
  Carrier L c= {v} by Def4;
  then
A1: Carrier L = {} or Carrier L = {v} by ZFMISC_1:33;
  assume L is convex;
  hence thesis by A1,Th77,Th80;
end;
