%   ORIGINAL: h4/arithmetic/DIV__1
% 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/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/arithmetic/DIV__ONE: !q. h4/arithmetic/DIV q (h4/num/SUC h4/num/0) = q
% Goal: !q. h4/arithmetic/DIV q (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = q
%   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_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_arithmetics_DIVu_u_ONE]: !q. h4/arithmetic/DIV q (h4/num/SUC h4/num/0) = q
% Goal: !q. h4/arithmetic/DIV q (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = q
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_Q310298,TV_Q310294]: ![V_f, V_g]: (![V_x]: s(TV_Q310294,happ(s(t_fun(TV_Q310298,TV_Q310294),V_f),s(TV_Q310298,V_x))) = s(TV_Q310294,happ(s(t_fun(TV_Q310298,TV_Q310294),V_g),s(TV_Q310298,V_x))) => s(t_fun(TV_Q310298,TV_Q310294),V_f) = s(t_fun(TV_Q310298,TV_Q310294),V_g))).
fof(ah4s_arithmetics_ONE, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_arithmetics_DIVu_u_ONE, axiom, ![V_q]: s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_q),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_nums_num,V_q)).
fof(ch4s_arithmetics_DIVu_u_1, conjecture, ![V_q]: s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_q),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,V_q)).
