
theorem
  for G1, G2, H1, H2 being non empty multMagma, f being Function of G1,
  H1, g being Function of G2,H2, x1 being Element of G1, x2 being Element of G2
  holds Gr2Iso(f,g).<*x1,x2*> = <*f.x1,g.x2*>
proof
  let G1, G2, H1, H2 be non empty multMagma, f be Function of G1,H1, g be
  Function of G2,H2, x1 be Element of G1, x2 be Element of G2;
  consider y1 being Element of G1, y2 being Element of G2 such that
A1: <*y1,y2*> = <*x1,x2*> and
A2: Gr2Iso(f,g).<*x1,x2*> = <*f.y1,g.y2*> by Def1;
  x1 = y1 by A1,FINSEQ_1:77;
  hence thesis by A1,A2,FINSEQ_1:77;
end;
