reserve X for OrtAfPl;
reserve o,a,a1,a2,a3,a4,b,b1,b2,b3,b4,c,c1,c2,c3,d,d1,d2,d3,d4,e1,e2 for
  Element of X;
reserve a29,a39,b29,x9 for Element of the AffinStruct of X;
reserve A,K,M,N for Subset of X;
reserve A9,K9 for Subset of the AffinStruct of X;

theorem Th6:
  for a,b,c,d,M holds for M9 being Subset of the AffinStruct of X, c9,d9 being
Element of the AffinStruct of X
  st c =c9 & d=d9 & M=M9 & a in M & b in M & c9,d9 // M9 holds c,d // a,b
proof
  let a,b,c,d,M;
  let M9 be Subset of the AffinStruct of X,
      c9,d9 be Element of the AffinStruct of X such that
A1: c =c9 and
A2: d=d9 and
A3: M=M9 and
A4: a in M and
A5: b in M and
A6: c9,d9 // M9;
  reconsider a9=a,b9=b as Element of the AffinStruct of X;
A7:  M9 is being_line by A6,AFF_1:26;
  then a9,b9 // M9 by A3,A4,A5,AFF_1:52;
  then c9,d9 // a9,b9 by A7,A6,AFF_1:31;
  hence thesis by A1,A2,ANALMETR:36;
end;
