theorem
  x<>y & Mid x,y,z & Mid x,y,t implies Mid y,z,t or Mid y,t,z
proof
  assume
A1: x<>y;
  assume Mid x,y,z & Mid x,y,t;
  then x,y // y,z & x,y // y,t;
  then y,z // y,t by A1,ANALOAF:def 5;
  hence thesis by Th7;
end;
