Okay, what is N1, as distinct from a special case of N2?
Let me try again to answer this. Let's see if I can keep straight what N1
stands for this time.
IMHO it is quite an easy lemma to show that N1 is a special case of N2,
namely the zero-acceleration case. That suffices to answer Carl's question.
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Tangential comments:
1) Just because it is a special case of another law, that doesn't mean it
can't be considered a law itself. The laws of electrostatics are a special
case of the laws of electrodynamics. Classical kinematics is a special
case of relativistic kinematics. Classical mechanics is a special case of
quantum mechanics. No problem.
2) There are several elements of what we normally consider "Newtonian
mechanics" that are not captured by Newton's laws. In particular, there
are a bunch of "existence axioms":
-- we need to stipulate that reference frames exist, have certain
properties, and can be constructed operationally, with good consistency
and reproducibility.
-- we need to stipulate that forces exist, have certain properties, and
can be measured operationally, with good consistency and reproducibility.
Many of these ideas go back to Galileo.
So, when laying out the foundations of mechanics, one need not and should
not pretend that Newton's laws are the whole story, or that they magically
mean something beyond what the words say.