reserve X for BCI-algebra;
reserve n for Nat;
reserve x,y for Element of X;
reserve a,b for Element of AtomSet(X);
reserve m,n for Nat;
reserve i,j for Integer;

theorem
  (a\b)|^(-n) = a|^(-n)\(b|^(-n))
proof
  set c = a`, d = b`;
  reconsider c,d as Element of AtomSet(X) by BCIALG_1:34;
A1: c|^n = a|^(-n) & d|^n = b |^ (-n) by Th10;
  (a\b)|^(-n)=((a\b)`)|^n by Th10
    .=(a`\b`)|^n by BCIALG_1:9;
  hence thesis by A1,Th15;
end;
