reserve AFV for WeakAffVect;
reserve a,b,c,d,e,f,a9,b9,c9,d9,f9,p,q,r,o,x99 for Element of AFV;

theorem Th20:
  Mid a,b,c & Mid a,b9,c implies b =b9 or MDist b,b9
proof
  assume that
A1: Mid a,b,c and
A2: Mid a,b9,c;
A3: a,b // b,c by A1;
  consider d such that
A4: b9,c // b,d by Def1;
A5: b,d // b9,c by A4,Th3;
  then b,b9 // d,c by Def1;
  then
A6: b9,b // c,d by Th7;
  a,b9 // b9,c by A2;
  then a,b9 // b,d by A5,Def1;
  then b,b9 // c,d by A3,Def1;
  then b,b9 // b9,b by A6,Def1;
  hence thesis;
end;
