proposition: Lemma conj_nth_rp (i : 'I_d) : conjL (rp`_i) = rp`_(tperm i0 i1 i).
proof: Proof. rewrite permE/=; case: eqVneq => [->|Ni0]; first by rewrite conj_rp0. case: eqVneq => [->|Ni1]; first by rewrite conj_rp1. have i_gt : (i > 1)%N by case: i Ni0 Ni1 => [[|[|[]]]]. apply: (fmorph_inj iota); rewrite iotaJ. by rewrite conj_Creal ?nth_rp_real// tpermD// -val_eqE/= ltn_eqF// ltnW. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field polyrcf) Abel(various classic_ext map_gal algR) Abel(char0 cyclotomic_ext real_closed_ext)