reserve x,y for set;
reserve X for non empty set;
reserve a,b,c,d for Element of X;
reserve S for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u,w for Element of S;

theorem
  x<>y & Mid x,y,z & Mid x,y,t implies Mid x,z,t or Mid x,t,z
proof
  assume
A1: x<>y;
  assume that
A2: Mid x,y,z and
A3: Mid x,y,t;
  x,y // y,t by A3;
  then
A4: x,y // x,t by ANALOAF:def 5;
  x,y // y,z by A2;
  then x,y // x,z by ANALOAF:def 5;
  then x,z // x,t by A1,A4,ANALOAF:def 5;
  hence thesis by Th7;
end;
