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
  a,b // a9,b9 & c,d // c9,d9 & b,f // c,d & b9,f9 // c9,d9 implies a,f
  // a9,f9
proof
  assume that
A1: a,b // a9,b9 and
A2: c,d // c9,d9 and
A3: b,f // c,d and
A4: b9,f9 // c9,d9;
  b9,f9 // c,d by A2,A4,Def1;
  then
A5: b,f // b9,f9 by A3,Def1;
  b,a // b9,a9 by A1,Th7;
  hence thesis by A5,Def1;
end;
