theorem
  f=v & g=u implies f+g=v+u
proof
  assume
A1: f=v & g=u;
  reconsider v2=v, u2=u as VECTOR of CLSp_L1Funct M by TARSKI:def 3;
  thus v+u=v2+u2 by ZFMISC_1:87,FUNCT_1:49
    .=f+g by A1,Th19;
end;
