%   ORIGINAL: h4/complex/COMPLEX__EQ__LMUL__IMP
% 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/complex/COMPLEX__MUL__COMM: !z w. h4/complex/complex__mul z w = h4/complex/complex__mul w z
% Assm: h4/complex/COMPLEX__EQ__RMUL__IMP: !z w v. ~(z = h4/complex/complex__of__num h4/num/0) /\ h4/complex/complex__mul w z = h4/complex/complex__mul v z ==> w = v
% Goal: !z w v. ~(z = h4/complex/complex__of__num h4/num/0) /\ h4/complex/complex__mul z w = h4/complex/complex__mul z v ==> w = v
%   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_complexs_COMPLEXu_u_MULu_u_COMM]: !z w. h4/complex/complex__mul z w = h4/complex/complex__mul w z
% Assm [h4s_complexs_COMPLEXu_u_EQu_u_RMULu_u_IMP]: !z w v. ~(z = h4/complex/complex__of__num h4/num/0) /\ h4/complex/complex__mul w z = h4/complex/complex__mul v z ==> w = v
% Goal: !z w v. ~(z = h4/complex/complex__of__num h4/num/0) /\ h4/complex/complex__mul z w = h4/complex/complex__mul z v ==> w = v
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_Q257257,TV_Q257253]: ![V_f, V_g]: (![V_x]: s(TV_Q257253,happ(s(t_fun(TV_Q257257,TV_Q257253),V_f),s(TV_Q257257,V_x))) = s(TV_Q257253,happ(s(t_fun(TV_Q257257,TV_Q257253),V_g),s(TV_Q257257,V_x))) => s(t_fun(TV_Q257257,TV_Q257253),V_f) = s(t_fun(TV_Q257257,TV_Q257253),V_g))).
fof(ah4s_complexs_COMPLEXu_u_MULu_u_COMM, axiom, ![V_z, V_w]: s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(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),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_z)))).
fof(ah4s_complexs_COMPLEXu_u_EQu_u_RMULu_u_IMP, axiom, ![V_z, V_w, V_v]: ((~ (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_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w),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_mul(s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v),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),V_w) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))).
fof(ch4s_complexs_COMPLEXu_u_EQu_u_LMULu_u_IMP, conjecture, ![V_z, V_w, V_v]: ((~ (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_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) & s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(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),V_w))) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_complexs_complexu_u_mul(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),V_v)))) => s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_w) = s(t_h4s_pairs_prod(t_h4s_realaxs_real,t_h4s_realaxs_real),V_v))).
