reserve C for CategoryStr;
reserve f,f1,f2,f3 for morphism of C;
reserve g1,g2 for morphism of C opp;

theorem Th21:
  for C being discrete CategoryStr, f1,f2 being morphism of C
  st f1 |> f2 holds f1 = f2 & f1 (*) f2 = f2
  proof
    let C be discrete CategoryStr;
    let f1,f2 be morphism of C;
    assume
A1: f1 |> f2;
    f2 is identity by Def15;
    then
A2: f1 (*) f2 = f1 by Def5,A1;
    f1 is identity by Def15;
    hence thesis by A2,A1,Def4;
  end;
