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