theorem Th36:
  for a,b,c,d being Element of POS, a9,b9,c9,d9 being Element of
  the AffinStruct of POS st a=a9& b=b9 & c = c9 & d=d9
   holds (a,b // c,d iff a9,b9 // c9,d9)
proof
  set AF = the AffinStruct of POS;
  let a,b,c,d be Element of POS, a9,b9,c9,d9 be Element of the AffinStruct of
  POS such that
A1: a=a9 & b=b9 & c = c9 & d=d9;
  hereby
    assume a,b // c,d;
    then [[a9,b9],[c9,d9]] in the CONGR of AF by A1,ANALOAF:def 2;
    hence a9,b9 // c9,d9 by ANALOAF:def 2;
  end;
  assume a9,b9 // c9,d9;
  then [[a,b],[c,d]] in the CONGR of POS by A1,ANALOAF:def 2;
  hence thesis by ANALOAF:def 2;
end;
