reserve MS for OrtAfPl;
reserve MP for OrtAfSp;

theorem Th2:
  for a,b,c,d being Element of MS, K being Subset of the carrier of
  MS st a,b _|_ K & c,d _|_ K holds a,b // c,d & a,b // d,c
proof
  let a,b,c,d be Element of MS, K be Subset of MS such that
A1: a,b _|_ K and
A2: c,d _|_ K;
  reconsider K9=K as Subset of the AffinStruct of MS;
  K is being_line by A1,ANALMETR:44;
  then K9 is being_line by ANALMETR:43;
  then consider p9,q9 being Element of the AffinStruct of MS such that
A3: p9 in K9 & q9 in K9 and
A4: p9 <> q9 by AFF_1:19;
  reconsider p=p9,q=q9 as Element of MS;
  a,b _|_ p,q & c,d _|_ p,q by A1,A2,A3,ANALMETR:53;
  hence a,b // c,d by A4,ANALMETR:63;
  hence thesis by ANALMETR:59;
end;
