theorem Th64:
  cod f = a implies y .--> f is Injections_family of a,{y}
proof
  set F = y .--> f;
  assume
A1: cod f = a;
  now
    let x;
    assume
A2: x in {y};
    hence (cods F)/.x = cod(F/.x) by Def2
      .= a by A1,A2,Th2
      .= (y .--> a)/.x by A2,Th2;
  end;
  hence cods F = {y} --> a by Th1;
end;
