theorem
 for f being Morphism of d,c
  st c is_a_product_wrt p1,p2 & dom f = d & cod f = c & f is invertible
 holds d is_a_product_wrt p1(*)f,p2(*)f
proof
 let f be Morphism of d,c such that
A1: c is_a_product_wrt p1,p2 and
A2: dom f = d & cod f = c & f is invertible;
  c is_a_product_wrt (0,{0})-->(p1,p2) by A1,Th54;
  then d is_a_product_wrt ((0,{0})-->(p1,p2))*f by A2,Th51;
  then d is_a_product_wrt (0,{0})-->(p1(*)f,p2(*)f) by Th14;
  hence thesis by Th54;
end;
