reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;
reserve p,q for natural Number;
reserve i0,i,i1,i2,i4 for Integer;
reserve x for set;
reserve p for Prime;
reserve i for Nat;
reserve x for Real;
reserve k for Nat;
reserve k,n,n1,n2,m1,m2 for Nat;

theorem
  k <= n implies m |^ k divides m |^ n
proof
  assume k <= n;
  then consider t being Nat such that
A1: n = k + t by NAT_1:10;
  reconsider t as Element of NAT by ORDINAL1:def 12;
  m |^ n = (m |^ k)*(m |^ t) by A1,Th8;
  hence thesis by NAT_D:def 3;
end;
