reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve C for Category;
reserve O for non empty Subset of the carrier of C;

theorem Th7:
  for G1,G2,G3 being non empty addMagma, f being Function of G1,
  G2, g being Function of G2,G3 st f is additive & g is additive holds g*f is
  additive
proof
  let G1,G2,G3 be non empty addMagma, f be Function of G1,G2, g be Function
  of G2,G3 such that
A1: f is additive and
A2: g is additive;
  set h = g*f;
  now
    let x,y be Element of G1;
A3: g.(f.x) = h.x & g.(f.y) = h.y by FUNCT_2:15;
    thus h.(x+y) = g.(f.(x+y)) by FUNCT_2:15
      .= g.(f.x+f.y) by A1
      .= h.x+h.y by A2,A3;
  end;
  hence thesis;
end;
