%   ORIGINAL: h4/numeral__bit/NUMERAL__TIMES__2EXP_c0
% 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/arithmetic/MULT__CLAUSES_c0: !m. h4/arithmetic/_2A h4/num/0 m = h4/num/0
% Assm: h4/bit/TIMES__2EXP__def: !x n. h4/bit/TIMES__2EXP x n = h4/arithmetic/_2A n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Goal: !n. h4/bit/TIMES__2EXP n h4/num/0 = h4/num/0
%   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_arithmetics_MULTu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2A h4/num/0 m = h4/num/0
% Assm [h4s_bits_TIMESu_u_2EXPu_u_def]: !x n. h4/bit/TIMES__2EXP x n = h4/arithmetic/_2A n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Goal: !n. h4/bit/TIMES__2EXP n h4/num/0 = h4/num/0
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_Q16202,TV_Q16198]: ![V_f, V_g]: (![V_x]: s(TV_Q16198,happ(s(t_fun(TV_Q16202,TV_Q16198),V_f),s(TV_Q16202,V_x))) = s(TV_Q16198,happ(s(t_fun(TV_Q16202,TV_Q16198),V_g),s(TV_Q16202,V_x))) => s(t_fun(TV_Q16202,TV_Q16198),V_f) = s(t_fun(TV_Q16202,TV_Q16198),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_arithmetics_MULTu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bits_TIMESu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_x)))))).
fof(ch4s_numeralu_u_bits_NUMERALu_u_TIMESu_u_2EXPu_c0, conjecture, ![V_n]: s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
