proposition: Lemma gt0_alg_nlt0 x : lt_alg zero_alg x -> ~~ lt_alg x zero_alg.
proof: Proof. rewrite -[x]reprK !piE -!(rwP lt_algcrealP, rwP le_algcrealP). move=> hx; pose_big_enough i. apply: (@le_crealP _ i)=> j /= hj. by rewrite ltW // creal_gt0_always. by close. 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)