
theorem Th22:
  for C1, C2 being non empty AltGraph,
  F being Covariant FunctorStr over C1,C2, o1,o2 being Object of C1
  holds (the ObjectMap of F).(o1,o2) = [F.o1,F.o2]
proof
  let C1, C2 be non empty AltGraph, F be Covariant FunctorStr over C1,C2,
  o1,o2 be Object of C1;
  the ObjectMap of F is Covariant by Def12;
  then consider f being Function of the carrier of C1, the carrier of C2 such
  that
A1: the ObjectMap of F = [:f,f:];
A2: F.o1 = ([f.o1,f.o1])`1 by A1,FUNCT_3:75
    .= f.o1;
  F.o2 = ([f.o2,f.o2])`1 by A1,FUNCT_3:75
    .= f.o2;
  hence thesis by A1,A2,FUNCT_3:75;
end;
