proposition: Lemma imaginary_exists : {i : F | i ^+ 2 = -1}.
proof: Proof. have /sig_eqW[i Di2] := @solve_monicpoly F 2 (nth 0 [:: -1]) isT. by exists i; rewrite Di2 !big_ord_recl big_ord0 mul0r mulr1 !addr0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)