theorem
  c is_a_coproduct_wrt i1,i2 & d is_a_coproduct_wrt j1,j2 & dom i1 = dom
  j1 & dom i2 = dom j2 implies c,d are_isomorphic
proof
  assume that
A1: c is_a_coproduct_wrt i1,i2 and
A2: d is_a_coproduct_wrt j1,j2 and
A3: dom i1 = dom j1 & dom i2 = dom j2;
  set I = {0,{0}}, F = (0,{0})-->(i1,i2), F9 = (0,{0})-->(j1,j2);
A4: c is_a_coproduct_wrt F & d is_a_coproduct_wrt F9 by A1,A2,Th79;
  doms F = (0,{0})-->(dom j1,dom j2) by A3,Th6
    .= doms F9 by Th6;
  hence thesis by A4,Th72;
end;
