
theorem Th17:
  for I1 being set, I2,I3 being non empty set,
  f being Function of I1,I2, g being Function of I2,I3,
  B being ManySortedSet of I2, C being ManySortedSet of I3,
  G being MSUnTrans of g,B,C holds G*f is MSUnTrans of g*f,B*f,C
proof
  let I1 be set, I2,I3 be non empty set,
  f be Function of I1,I2, g be Function of I2,I3,
  B be ManySortedSet of I2, C be ManySortedSet of I3, G be MSUnTrans of g,B,C;
A1: C*(g*f) = C*g*f by RELAT_1:36;
  G is ManySortedFunction of B,C*g by Def4;
  hence G*f is ManySortedFunction of B*f,C*(g*f) by A1,ALTCAT_2:5;
end;
