%   ORIGINAL: h4/bit/DIVMOD__2EXP0
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bit/MOD__2EXP__def: !x n. h4/bit/MOD__2EXP x n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm: h4/bit/DIV__2EXP__def: !x n. h4/bit/DIV__2EXP x n = h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm: h4/bit/DIVMOD__2EXP__def: !x n. h4/bit/DIVMOD__2EXP x n = h4/pair/_2C (h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)) (h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x))
% Goal: !x n. h4/bit/DIVMOD__2EXP x n = h4/pair/_2C (h4/bit/DIV__2EXP x n) (h4/bit/MOD__2EXP x n)
%   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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bits_MODu_u_2EXPu_u_def]: !x n. h4/bit/MOD__2EXP x n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm [h4s_bits_DIVu_u_2EXPu_u_def]: !x n. h4/bit/DIV__2EXP x n = h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm [h4s_bits_DIVMODu_u_2EXPu_u_def]: !x n. h4/bit/DIVMOD__2EXP x n = h4/pair/_2C (h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)) (h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x))
% Goal: !x n. h4/bit/DIVMOD__2EXP x n = h4/pair/_2C (h4/bit/DIV__2EXP x n) (h4/bit/MOD__2EXP x n)
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_Q200590,TV_Q200586]: ![V_f, V_g]: (![V_x]: s(TV_Q200586,happ(s(t_fun(TV_Q200590,TV_Q200586),V_f),s(TV_Q200590,V_x))) = s(TV_Q200586,happ(s(t_fun(TV_Q200590,TV_Q200586),V_g),s(TV_Q200590,V_x))) => s(t_fun(TV_Q200590,TV_Q200586),V_f) = s(t_fun(TV_Q200590,TV_Q200586),V_g))).
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_bits_MODu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_mod(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(ah4s_bits_DIVu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_divu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_div(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(ah4s_bits_DIVMODu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_bits_divmodu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_arithmetics_div(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))))),s(t_h4s_nums_num,h4s_arithmetics_mod(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_bits_DIVMODu_u_2EXP0, conjecture, ![V_x, V_n]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_bits_divmodu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_bits_divu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n)))))).
