theorem Th39:
  a is initial & dom f = a & cod f = b implies init(a,b) = f
proof
  assume that
A1: a is initial and
A2: dom f = a & cod f = b;
  consider h being Morphism of a,b such that
A3: for g being Morphism of a,b holds h = g by A1;
  f is Morphism of a,b by A2,CAT_1:4;
  hence f = h by A3
    .= init(a,b) by A3;
end;
