theorem Th5:
  A is being_line & M is being_line & a in A & b in A & a in M & b
  in M implies a=b or A=M
proof
  assume that
A1: A is being_line and
A2: M is being_line and
A3: a in A and
A4: b in A and
A5: a in M and
A6: b in M;
  reconsider A9=A,M9=M as Subset of the AffinStruct of X;
A7: M9 is being_line by A2,ANALMETR:43;
  assume
A8: a<>b;
  A9 is being_line by A1,ANALMETR:43;
  hence thesis by A3,A4,A5,A6,A8,A7,AFF_1:18;
end;
