reserve AFV for WeakAffVect;
reserve a,a9,b,b9,c,d,p,p9,q,q9,r,r9 for Element of AFV;
reserve AFV for WeakAffSegm;
reserve a,b,b9,b99,c,d,p,p9 for Element of AFV;

theorem Th5:
  for a,b holds a,a // b,b
proof
  let a,b;
  now
    consider c such that
A1: a,c // c,b by Def1;
    assume
A2: a<>b;
    c,a // c,b by A1,Th4;
    hence thesis by A2,Def1;
  end;
  hence thesis by Def1;
end;
