reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;

theorem Th1:
  f in Hom(a,b) iff dom(f)=a & cod(f)=b
proof
  thus f in Hom(a,b) implies dom(f) = a & cod(f) = b
  proof
    assume f in Hom(a,b);
    then ex g st f = g & dom(g) = a & cod(g) = b;
    hence thesis;
  end;
  thus thesis;
end;
