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
  Mid a,b,c implies a,b,c are_collinear
proof
  assume Mid a,b,c;
  then a,b // b,c;
  then a,b // a,c by ANALOAF:def 5;
  then a,b '||' a,c;
  hence thesis;
end;
