[STATEMENT]
lemma conductor_principal [simp]: "\<chi> = principal_dchar n \<Longrightarrow> conductor = 1"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. \<chi> = principal_dchar n \<Longrightarrow> conductor = 1
[PROOF STEP]
by (subst conductor_eq_1_iff_principal)