theorem
  a,b,c are_collinear implies Mid a,b,c or Mid b,a,c or Mid a,c,b
proof
A1: a,b // c,a implies Mid b,a,c by ANALOAF:def 5;
  assume a,b,c are_collinear;
  then
A2: a,b '||' a,c;
  a,b // a,c implies ( Mid a,b,c or Mid a,c,b) by Th7;
  hence thesis by A2,A1;
end;
