Explicit `bigop` enumeration handling

Added lemmas `big_enum_cond`, `big_enum` and `big_enumP` to handle more
explicitly big ops iterating over explicit enumerations in a `finType`.
   The previous practice was to rely on the convertibility between
`enum A` and `filter A (index_enum T)`, sometimes explicitly via the
`filter_index_enum` equality, more often than not implicitly.
  Both are likely to fail after the integration of `finmap`, as the
`choiceType` theory can’t guarantee that the order in selected
enumerations is consistent.
  For this reason `big_enum` and the related (but currently unused)
`big_image` lemmas are restricted to the abelian case. The `big_enumP`
lemma can be used to handle enumerations in the non-abelian case, as
explained in the `bigop.v` internal documentation.
  The Changelog entry enjoins clients to stop relying on either
`filter_index_enum` and convertibility (though this PR still provides
both), and warns about the restriction of the `big_image` lemma set to
the abelian case, as it it a possible source of incompatibility.

1 files changed, 4 insertions, 1 deletions

diff --git a/mathcomp/algebra/poly.v b/mathcomp/algebra/poly.v
index 2bb3614..25037e8 100644
--- a/mathcomp/algebra/poly.v
+++ b/mathcomp/algebra/poly.v
@@ -922,7 +922,10 @@ by rewrite size_XsubC.
 Qed.
 
 Lemma size_exp_XsubC n a : size (('X - a%:P) ^+ n) = n.+1.
-Proof. by rewrite -[n]card_ord -prodr_const size_prod_XsubC cardE enumT. Qed.
+Proof.
+rewrite -[n]card_ord -prodr_const -big_filter size_prod_XsubC.
+by have [e _ _ [_ ->]] := big_enumP.
+Qed.
 
 (* Some facts about regular elements. *)