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;
reserve o,m for set;
reserve B,C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,f1,f2,g,g1,g2 for Morphism of C;
reserve f,f1,f2 for Morphism of a,b;
reserve f9 for Morphism of b,a;
reserve g for Morphism of b,c;
reserve h,h1,h2 for Morphism of c,d;

theorem
  Hom(a,b) <> {} & a is terminal implies f is monic
proof
  assume that
A1: Hom(a,b) <> {} and
A2: a is terminal;
  now
    let c be (Object of C),g,h be Morphism of c,a such that
    Hom(c,a)<>{} and
    f*g=f*h;
    consider ff being Morphism of c,a such that
A3: for gg being Morphism of c,a holds ff=gg by A2;
    ff = g by A3;
    hence g=h by A3;
  end;
  hence thesis by A1;
end;
