Arguments mxmoduleP {m U}.

(* Specifications: *)
Lemma rstabS m1 m2 (U : 'M_(m1, n)) (V : 'M_(m2, n)) :
(U <= V)%MS -> rstab rG V \subset rstab rG U.
Lemma eqmx_rstab m1 m2 (U : 'M_(m1, n)) (V : 'M_(m2, n)) :
(U :=: V)%MS -> rstab rG U = rstab rG V.
Lemma mxmodule_eigenvector m (U : 'M_(m, n)) :
mxmodule U -> \rank U = 1%N ->
{u : 'rV_n & {a | (U :=: u)%MS & {in G, forall x, u *m rG x = a x *: u}}}.
Lemma addsmx_module m1 m2 U V :
@mxmodule m1 U -> @mxmodule m2 V -> mxmodule (U + V)%MS.
Lemma sumsmx_module I r (P : pred I) U :
(forall i, P i -> mxmodule (U i)) -> mxmodule (\sum_(i <- r | P i) U i)%MS.
Lemma capmx_module m1 m2 U V :
@mxmodule m1 U -> @mxmodule m2 V -> mxmodule (U :&: V)%MS.
Lemma bigcapmx_module I r (P : pred I) U :
(forall i, P i -> mxmodule (U i)) -> mxmodule (\bigcap_(i <- r | P i) U i)%MS.