%   ORIGINAL: h4/numeral/DIV2__BIT1
% 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/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/numeral/numeral__div2_c0: h4/arithmetic/DIV2 h4/num/0 = h4/num/0
% Assm: h4/numeral/numeral__div2_c1: !n. h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = h4/arithmetic/NUMERAL n
% Assm: h4/numeral/numeral__div2_c2: !n. h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Goal: !x. h4/arithmetic/DIV2 (h4/arithmetic/BIT1 x) = 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_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_numerals_numeralu_u_div2u_c0]: h4/arithmetic/DIV2 h4/num/0 = h4/num/0
% Assm [h4s_numerals_numeralu_u_div2u_c1]: !n. h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = h4/arithmetic/NUMERAL n
% Assm [h4s_numerals_numeralu_u_div2u_c2]: !n. h4/arithmetic/DIV2 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = h4/arithmetic/NUMERAL (h4/num/SUC n)
% Goal: !x. h4/arithmetic/DIV2 (h4/arithmetic/BIT1 x) = 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_Q318034,TV_Q318030]: ![V_f, V_g]: (![V_x]: s(TV_Q318030,happ(s(t_fun(TV_Q318034,TV_Q318030),V_f),s(TV_Q318034,V_x))) = s(TV_Q318030,happ(s(t_fun(TV_Q318034,TV_Q318030),V_g),s(TV_Q318034,V_x))) => s(t_fun(TV_Q318034,TV_Q318030),V_f) = s(t_fun(TV_Q318034,TV_Q318030),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_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_numerals_numeralu_u_div2u_c0, axiom, s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_numerals_numeralu_u_div2u_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_div2u_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))).
fof(ch4s_numerals_DIV2u_u_BIT1, conjecture, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_x))))) = s(t_h4s_nums_num,V_x)).
