%   ORIGINAL: h4/complex/COMPLEX__RSCALAR__RMUL__SUB
% 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/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/complex/COMPLEX__SCALAR__LMUL__SUB: !z l k. h4/complex/complex__scalar__lmul (h4/real/real__sub k l) z = h4/complex/complex__sub (h4/complex/complex__scalar__lmul k z) (h4/complex/complex__scalar__lmul l z)
% Assm: h4/complex/COMPLEX__SCALAR__MUL__COMM: !z k. h4/complex/complex__scalar__lmul k z = h4/complex/complex__scalar__rmul z k
% Goal: !z l k. h4/complex/complex__scalar__rmul z (h4/real/real__sub k l) = h4/complex/complex__sub (h4/complex/complex__scalar__rmul z k) (h4/complex/complex__scalar__rmul z l)
%   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_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_SUB]: !z l k. h4/complex/complex__scalar__lmul (h4/real/real__sub k l) z = h4/complex/complex__sub (h4/complex/complex__scalar__lmul k z) (h4/complex/complex__scalar__lmul l z)
% Assm [h4s_complexs_COMPLEXu_u_SCALARu_u_MULu_u_COMM]: !z k. h4/complex/complex__scalar__lmul k z = h4/complex/complex__scalar__rmul z k
% Goal: !z l k. h4/complex/complex__scalar__rmul z (h4/real/real__sub k l) = h4/complex/complex__sub (h4/complex/complex__scalar__rmul z k) (h4/complex/complex__scalar__rmul z l)
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_Q258982,TV_Q258978]: ![V_f, V_g]: (![V_x]: s(TV_Q258978,happ(s(t_fun(TV_Q258982,TV_Q258978),V_f),s(TV_Q258982,V_x))) = s(TV_Q258978,happ(s(t_fun(TV_Q258982,TV_Q258978),V_g),s(TV_Q258982,V_x))) => s(t_fun(TV_Q258982,TV_Q258978),V_f) = s(t_fun(TV_Q258982,TV_Q258978),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_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_complexs_COMPLEXu_u_SCALARu_u_LMULu_u_SUB, axiom, ![V_z, V_l, V_k]: 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_realu_u_sub(s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,V_l))),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_complexs_complexu_u_sub(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_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_lmul(s(t_h4s_realaxs_real,V_l),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))))).
fof(ah4s_complexs_COMPLEXu_u_SCALARu_u_MULu_u_COMM, axiom, ![V_z, V_k]: 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_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_rmul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_realaxs_real,V_k)))).
fof(ch4s_complexs_COMPLEXu_u_RSCALARu_u_RMULu_u_SUB, conjecture, ![V_z, V_l, V_k]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_rmul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_k),s(t_h4s_realaxs_real,V_l))))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_sub(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_rmul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_realaxs_real,V_k))),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_scalaru_u_rmul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z),s(t_h4s_realaxs_real,V_l)))))).
