From 0b1ea03dafcf36880657ba910eec28ab78ccd018 Mon Sep 17 00:00:00 2001
From: Georges Gonthier
Date: Thu, 13 Dec 2018 12:55:43 +0100
Subject: 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.
---
 mathcomp/algebra/intdiv.v | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'mathcomp/algebra/intdiv.v')

diff --git a/mathcomp/algebra/intdiv.v b/mathcomp/algebra/intdiv.v
index 2f5e844..1da8313 100644
--- a/mathcomp/algebra/intdiv.v
+++ b/mathcomp/algebra/intdiv.v
@@ -714,7 +714,7 @@ rewrite mul1n; apply/dvdn_biggcdP/(all_nthP 0)=> a_dv_p i ltip /=.
 exact: a_dv_p.
 Qed.
 
-Lemma map_poly_divzK a p :
+Lemma map_poly_divzK {a} p :
   p \is a polyOver (dvdz a) -> a *: map_poly (divz^~ a) p = p.
 Proof.
 move/polyOverP=> a_dv_p; apply/polyP=> i.
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