Section LtmxIdentities.
Variables (m1 m2 n : nat) (A : 'M_(m1, n)) (B : 'M_(m2, n)).
Hint Resolve rank_leq_row rank_leq_col row_ebase_unit col_ebase_unit : core.
Arguments mulmx_max_rank [r m n].
Arguments submxP {m1 m2 n A B}.
Arguments row_subP {m1 m2 n A B}.
Arguments rV_subP {m1 m2 n A B}.
Arguments row_fullP {m n A}.
(* A variant of row_free_inj that exposes mulmxr, an alias for mulmx^~ *)
(* but which is canonically additive *)
Definition row_free_injr m n p A : row_free A -> injective (mulmxr A) :=
@row_free_inj m n p A.
Arguments eqmxP {m1 m2 n A B}.

Lemma rV_eqP m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) :
reflect (forall u : 'rV_n, (u <= A) = (u <= B))%MS (A == B)%MS.