proposition: Lemma root_inv_algcreal (x : algcreal) (x_neq0 : (x != 0)%CR) : ((annul_creal (div_algcreal (cst_algcreal 1) x)).[x_neq0^-1] == 0)%CR.
proof: Proof. rewrite /div_algcreal; case: eq_algcreal_dec=> [/(_ x_neq0)|x_neq0'] //=. case: simplify_algcreal=> x' px'0_neq0 [x'_neq0 eq_xx']. apply: is_root_annul_creal; rewrite /= -(@eq_creal_inv _ _ _ x_neq0) //. by apply: eq_crealP; exists m0=> * /=; rewrite div1r subrr normr0. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg ssrnum ssrint rat poly polydiv polyorder) mathcomp(perm matrix mxpoly polyXY binomial generic_quotient) mathcomp(cauchyreals separable zmodp bigenough)