%   ORIGINAL: h4/complex/DE__MOIVRE__THM
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/complex/COMPLEX__POW__L: !z n k. h4/complex/complex__pow (h4/complex/complex__scalar__lmul k z) n = h4/complex/complex__scalar__lmul (h4/real/pow k n) (h4/complex/complex__pow z n)
% Assm: h4/complex/DE__MOIVRE__LEMMA: !x n. h4/complex/complex__pow (h4/pair/_2C (h4/transc/cos x) (h4/transc/sin x)) n = h4/pair/_2C (h4/transc/cos (h4/realax/real__mul (h4/real/real__of__num n) x)) (h4/transc/sin (h4/realax/real__mul (h4/real/real__of__num n) x))
% Goal: !z n. h4/complex/complex__pow (h4/complex/complex__scalar__lmul (h4/complex/modu z) (h4/pair/_2C (h4/transc/cos (h4/complex/arg z)) (h4/transc/sin (h4/complex/arg z)))) n = h4/complex/complex__scalar__lmul (h4/real/pow (h4/complex/modu z) n) (h4/pair/_2C (h4/transc/cos (h4/realax/real__mul (h4/real/real__of__num n) (h4/complex/arg z))) (h4/transc/sin (h4/realax/real__mul (h4/real/real__of__num n) (h4/complex/arg z))))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_complexs_COMPLEXu_u_POWu_u_L]: !z n k. h4/complex/complex__pow (h4/complex/complex__scalar__lmul k z) n = h4/complex/complex__scalar__lmul (h4/real/pow k n) (h4/complex/complex__pow z n)
% Assm [h4s_complexs_DEu_u_MOIVREu_u_LEMMA]: !x n. h4/complex/complex__pow (h4/pair/_2C (h4/transc/cos x) (h4/transc/sin x)) n = h4/pair/_2C (h4/transc/cos (h4/realax/real__mul (h4/real/real__of__num n) x)) (h4/transc/sin (h4/realax/real__mul (h4/real/real__of__num n) x))
% Goal: !z n. h4/complex/complex__pow (h4/complex/complex__scalar__lmul (h4/complex/modu z) (h4/pair/_2C (h4/transc/cos (h4/complex/arg z)) (h4/transc/sin (h4/complex/arg z)))) n = h4/complex/complex__scalar__lmul (h4/real/pow (h4/complex/modu z) n) (h4/pair/_2C (h4/transc/cos (h4/realax/real__mul (h4/real/real__of__num n) (h4/complex/arg z))) (h4/transc/sin (h4/realax/real__mul (h4/real/real__of__num n) (h4/complex/arg z))))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q260907,TV_Q260903]: ![V_f, V_g]: (![V_x]: s(TV_Q260903,happ(s(t_fun(TV_Q260907,TV_Q260903),V_f),s(TV_Q260907,V_x))) = s(TV_Q260903,happ(s(t_fun(TV_Q260907,TV_Q260903),V_g),s(TV_Q260907,V_x))) => s(t_fun(TV_Q260907,TV_Q260903),V_f) = s(t_fun(TV_Q260907,TV_Q260903),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_complexs_COMPLEXu_u_POWu_u_L, axiom, ![V_z, V_n, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_pow(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_k),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_nums_num,V_n))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_k),s(t_h4s_nums_num,V_n))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_pow(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_complexs_DEu_u_MOIVREu_u_LEMMA, axiom, ![V_x, V_n]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_pow(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,V_x))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_x)))))))).
fof(ch4s_complexs_DEu_u_MOIVREu_u_THM, conjecture, ![V_z, V_n]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_pow(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,h4s_complexs_arg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))),s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,h4s_complexs_arg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_complexs_modu(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))),s(t_h4s_nums_num,V_n))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_pairs_u_2c(s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,h4s_complexs_arg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z))))))),s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,h4s_complexs_arg(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))))))))))).
