theorem
  f is dilatation implies for a,b,c
  holds LIN a,b,c iff LIN f.a,f.b,f.c
proof
  assume
A1: f is dilatation;
  let a,b,c;
  a,b // a,c iff f.a,f.b // f.a,f.c by A1,Th72;
  hence thesis by AFF_1:def 1;
end;
