I want to prove that $ L = {a^n b^m c^{ \lfloor \frac{n}{m} \rfloor } } $
isn't context free language, so I choose N - constant from lemma
so the word is $ w = a^N b^N c $ and $ w = uvxyz $
1 case
v and y contains only a $ v,y \in a^{*} $
and $ w_2 = a^{N+B} b^{N} c $ where $ B > 0 $ is it correct to say that it doesn't belong to language, because $ N + B \neq N $ ?
edit
or second version
$ v,y \in a^{*} $ so $w_0 = uv^0xy^0z = uxz $ and $ w_0 = a^{N-B}b^Nc $ which doesn't belong to language because $ \lfloor \frac{N-B}{N} \rfloor = 0 \neq 1 $
and what with case where $ v \in a^+ $ and $ y \in b^+ $
