Proposition (Cancellation of permutations).
For any term f
such that [[f]] =
[[p ; g]] we can find
f such that
f = p ; f
and [[f
]] =
[[g]].
Show by induction on p that
p ; p* = id, and
p* ; p = id.
If we let f
be
p* ; f, then it is routine to check
that it satisfies our requirements.