proposition: Lemma eq_subZnat_irr (a b : nat) (i j r t : Iirr G) : (a%:R *: 'chi_i - b%:R *: 'chi_j == a%:R *: 'chi_r - b%:R *: 'chi_t) = [|| a == 0 | i == r] && [|| b == 0 | j == t] || [&& i == j, r == t & a == b].
proof: Proof. rewrite -!scaleNr eq_addZ_irr oppr_eq0 opprK -addr_eq0 -natrD eqr_nat. by rewrite !pnatr_eq0 addn_eq0; case: a b => [|a] [|b]; rewrite ?andbF. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)