proposition: Lemma det_trig n (A : 'M[R]_n) : is_trig_mx A -> \det A = \prod_(i < n) A i i.
proof: Proof. elim/trigsqmx_ind => [|k x c B Bt IHB]; first by rewrite ?big_ord0 ?det_mx00. rewrite det_lblock big_ord_recl det_mx11 IHB//; congr (_ * _). by rewrite -[ord0](lshift0 _ 0) block_mxEul. by apply: eq_bigr => i; rewrite -!rshift1 block_mxEdr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg countalg finalg zmodp)