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 Th12:
  a,b // a9,b9 & a,c // c9,b9 implies b,c // c9,a9
proof
  assume that
A1: a,b // a9,b9 and
A2: a,c // c9,b9;
  consider d such that
A3: c9,b9 // a9,d by Def1;
  a9,d // c9,b9 by A3,Th3;
  then a,c // a9,d by A2,Def1;
  then
A4: b,c // b9,d by A1,Def1;
  c9,a9 // b9,d by A3,Def1;
  hence thesis by A4,Def1;
end;
