proposition: Lemma bareiss_key_lemma_sub m n k d (l: 'rV[R]_n) (c: 'cV[R]_m) (M: 'M[R]_(m,n)) (f1: 'I_k -> 'I_m) (f2: 'I_k -> 'I_n): d * (minor f1 f2 (d *: M - c *m l)) = d ^+ k * (minor (lift_pred f1) (lift_pred f2) (block_mx d%:M l c M)).
proof: Proof. by rewrite /minor submatrix_lift_block bareiss_key_lemma submatrix_add submatrix_scale submatrix_opp submatrix_mul. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq path ssralg) mathcomp(fintype perm choice matrix bigop zmodp poly polydiv mxpoly) CoqEAL(ssrcomplements minor dvdring)