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

theorem Th3:
  f1 = g1 & f2 = g2 & f1 |> f2 implies f1 (*) f2 = g2 (*) g1
  proof
    assume
A1: f1 = g1 & f2 = g2;
    assume
A2: f1 |> f2;
A3: g2 |> g1 by A1,A2,FUNCT_4:42;
    thus f1 (*) f2 = (the composition of C).(f1,f2) by A2,Def3
    .= (~the composition of C).(f2,f1) by A2,FUNCT_4:def 2
    .= g2 (*) g1 by A1,A3,Def3;
  end;
