Adjust implicits of cancellation lemmas

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.

1 files changed, 6 insertions, 1 deletions

diff --git a/mathcomp/algebra/vector.v b/mathcomp/algebra/vector.v
index c4c62c3..4766c74 100644
--- a/mathcomp/algebra/vector.v
+++ b/mathcomp/algebra/vector.v
@@ -1355,6 +1355,8 @@ Proof. by elim/big_rec2: _ => [|i _ f _ <-]; rewrite lfunE. Qed.
 
 End LfunZmodType.
 
+Arguments fun_of_lfunK {R aT rT}.
+
 Section LfunVectType.
 
 Variables (R : comRingType) (aT rT : vectType R).
@@ -1603,6 +1605,7 @@ Arguments lfunPn {K aT rT f g}.
 Arguments lker0P {K aT rT f}.
 Arguments eqlfunP {K aT rT f g v}.
 Arguments eqlfun_inP {K aT rT V f g}.
+Arguments limg_lfunVK {K aT rT f} [x] f_x.
 
 Section FixedSpace.
 
@@ -1718,6 +1721,8 @@ Qed.
 
 End LinearPreimage.
 
+Arguments lpreimK {K aT rT f} [W] fW.
+
 Section LfunAlgebra.
 (* This section is a bit of a place holder: the instances we build here can't *)
 (* be canonical because we are missing an interface for proper vectTypes,     *)
@@ -1944,7 +1949,7 @@ Canonical subvs_vectType := VectType K subvs_of subvs_vectMixin.
 End SubVector.
 Prenex Implicits vsval vsproj vsvalK.
 Arguments subvs_inj {K vT U} [x1 x2].
-Arguments vsprojK {K vT U} [x].
+Arguments vsprojK {K vT U} [x] Ux.
 
 Section MatrixVectType.