Question on pumping lemma


prove that L={0^i,1^j | i>j for all i,j} is not a regular language using pumping lemma


Choose x = 0P+11p, which is obviously in L.
Then x = u v w, |v| ≥1, |uv| ≤p, and every u vmw, for any m ≥0, is in L.
Considering m = 0, we know that u w is in L.
v consists of just 0s, and contains at least one 0.
So removing v removes at least one 0, which yields a string that is not in L