reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem Th28:
  n <> 0 & 1 <= k implies (n |^ k) div n = n |^ (k -'1)
proof
  assume that
A1: n <> 0 and
A2: 1 <= k;
A3: k - 1 >= 1 - 1 by A2,XREAL_1:9;
  k = k - 1 + 1 .= (k -'1) + 1 by A3,XREAL_0:def 2;
  then n |^ k = n*(n |^ (k -'1)) by NEWTON:6;
  hence thesis by A1,NAT_D:18;
end;
