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;
