%   ORIGINAL: h4/transc/TAN__NEG
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/real/real__div: !y x. h4/real/_2F x y = h4/realax/real__mul x (h4/realax/inv y)
% Assm: h4/real/REAL__NEG__LMUL: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/real__neg x) y
% Assm: h4/transc/SIN__NEG: !x. h4/transc/sin (h4/realax/real__neg x) = h4/realax/real__neg (h4/transc/sin x)
% Assm: h4/transc/COS__NEG: !x. h4/transc/cos (h4/realax/real__neg x) = h4/transc/cos x
% Assm: h4/transc/tan0: !x. h4/transc/tan x = h4/real/_2F (h4/transc/sin x) (h4/transc/cos x)
% Goal: !x. h4/transc/tan (h4/realax/real__neg x) = h4/realax/real__neg (h4/transc/tan x)
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_reals_realu_u_div]: !y x. h4/real/_2F x y = h4/realax/real__mul x (h4/realax/inv y)
% Assm [h4s_reals_REALu_u_NEGu_u_LMUL]: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/real__neg x) y
% Assm [h4s_transcs_SINu_u_NEG]: !x. h4/transc/sin (h4/realax/real__neg x) = h4/realax/real__neg (h4/transc/sin x)
% Assm [h4s_transcs_COSu_u_NEG]: !x. h4/transc/cos (h4/realax/real__neg x) = h4/transc/cos x
% Assm [h4s_transcs_tan0]: !x. h4/transc/tan x = h4/real/_2F (h4/transc/sin x) (h4/transc/cos x)
% Goal: !x. h4/transc/tan (h4/realax/real__neg x) = h4/realax/real__neg (h4/transc/tan x)
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_Q194961,TV_Q194957]: ![V_f, V_g]: (![V_x]: s(TV_Q194957,happ(s(t_fun(TV_Q194961,TV_Q194957),V_f),s(TV_Q194961,V_x))) = s(TV_Q194957,happ(s(t_fun(TV_Q194961,TV_Q194957),V_g),s(TV_Q194961,V_x))) => s(t_fun(TV_Q194961,TV_Q194957),V_f) = s(t_fun(TV_Q194961,TV_Q194957),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_reals_realu_u_div, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_transcs_SINu_u_NEG, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_transcs_COSu_u_NEG, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_transcs_tan0, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,V_x)))))).
fof(ch4s_transcs_TANu_u_NEG, conjecture, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,V_x)))))).
