reserve X for BCI-algebra;
reserve x,y,z,u,a,b for Element of X;
reserve IT for non empty Subset of X;

theorem
  for a being Element of AtomSet(X),x,y being Element of BranchV(a)
  holds x\y in BCK-part(X)
proof
  let a be Element of AtomSet(X),x,y be Element of BranchV(a);
  set b=a\a;
  b=0.X & x\y in BranchV(b) by Def5,Th39;
  hence thesis;
end;
