reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem LmY: for a,b be Integer holds
a divides b & b|^m divides c implies a|^m divides c
proof
  let a,b be Integer;
  assume
  A1: a divides b & b|^m divides c; then
  a gcd b = |.a.| by NEWTON02:3; then
  (a|^m gcd b|^m) = |.a.||^m by NEWTON027
  .= |.a|^m.| by TAYLOR_2:1; then
  a|^m divides b|^m by NEWTON02:3;
  hence thesis by A1,INT_2:9;
end;
