Like injectivity lemmas, instances of cancellation lemmas (whose
conclusion is `cancel ? ?`, `{in ?, cancel ? ?}`, `pcancel`, or
`ocancel`) are passed to
generic lemmas such as `canRL` or `canLR_in`. Thus such lemmas should
not have trailing on-demand implicits _just before_ the `cancel`
conclusion, as these would be inconvenient to insert (requiring
essentially an explicit eta-expansion).
We therefore use `Arguments` or `Prenex Implicits` directives to make
all such arguments maximally inserted implicits. We don’t, however make
other arguments implicit, so as not to spoil direct instantiation of
the lemmas (in, e.g., `rewrite -[y](invmK injf)`).
We have also tried to do this with lemmas whose statement matches a
`cancel`, i.e., ending in `forall x, g (E[x]) = x` (where pattern
unification will pick up `f = fun x => E[x]`).
We also adjusted implicits of a few stray injectivity
lemmas, and defined constants.
We provide a shorthand for reindexing a bigop with a permutation.
Finally we used the new implicit signatures to simplify proofs that
use injectivity or cancellation lemmas.