theorem
  Mid x,y,z & Mid y,x,z implies x=y
proof
  assume that
A1: Mid x,y,z and
A2: Mid y,x,z;
  x,y // y,z by A1;
  then
A3: x,y // x,z by ANALOAF:def 5;
  y,x // x,z by A2;
  then
A4: x,y // z,x by ANALOAF:def 5;
  x=z implies x=y by A1,Th8;
  hence thesis by A3,A4,Th5;
end;
