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 Th4:
  x |^ 1 = x
proof
  x |^ 1 = x|^(0+1) .= x\(x|^0)` by Def1
    .=x\(0.X)` by Def1
    .=x\0.X by BCIALG_1:def 5;
  hence thesis by BCIALG_1:2;
end;
