reserve f,g,h for Function,
  A for set;
reserve F for Function,
  B,x,y,y1,y2,z for set;
reserve x,z for object;

theorem Th25:
  F.:(f,g)*h = F.:(f*h, g*h)
proof
  thus F.:(f,g)*h = F*(<:f,g:>*h) by RELAT_1:36
    .= F.:(f*h, g*h) by FUNCT_3:55;
end;
