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
  g is monic & h is monic implies h*g is monic
proof
  assume that
A1: g is monic and
A2: h is monic;
A3: Hom(b,c)<>{} by A1;
A4: Hom(c,d)<>{} by A2;
A5: now
    let a,f1,f2 such that
A6: Hom(a,b)<>{} and
A7: (h*g)*f1 = (h*g)*f2;
A8: Hom(a,c) <> {} by A3,A6,Th19;
    h*(g*f1) = (h*g)*f1 & (h*g)*f2 = h*(g*f2) by A3,A4,A6,Th21;
    then g*f1 = g*f2 by A2,A7,A8;
    hence f1 = f2 by A1,A6;
  end;
  Hom(b,d) <> {} by A3,A4,Th19;
  hence thesis by A5;
end;
