%   ORIGINAL: h4/bit/BIT__OF__BITS__THM
% 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/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/bit/BIT__def: !n b. h4/bit/BIT b n <=> h4/bit/BITS b b n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bit/BITS__COMP__THM: !n l2 l1 h2 h1. h4/arithmetic/_3C_3D (h4/arithmetic/_2B h2 l1) h1 ==> h4/bit/BITS h2 l2 (h4/bit/BITS h1 l1 n) = h4/bit/BITS (h4/arithmetic/_2B h2 l1) (h4/arithmetic/_2B l2 l1) n
% Goal: !n l h a. h4/arithmetic/_3C_3D (h4/arithmetic/_2B l n) h ==> (h4/bit/BIT n (h4/bit/BITS h l a) <=> h4/bit/BIT (h4/arithmetic/_2B l n) a)
%   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_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_bits_BITu_u_def]: !n b. h4/bit/BIT b n <=> h4/bit/BITS b b n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bits_BITSu_u_COMPu_u_THM]: !n l2 l1 h2 h1. h4/arithmetic/_3C_3D (h4/arithmetic/_2B h2 l1) h1 ==> h4/bit/BITS h2 l2 (h4/bit/BITS h1 l1 n) = h4/bit/BITS (h4/arithmetic/_2B h2 l1) (h4/arithmetic/_2B l2 l1) n
% Goal: !n l h a. h4/arithmetic/_3C_3D (h4/arithmetic/_2B l n) h ==> (h4/bit/BIT n (h4/bit/BITS h l a) <=> h4/bit/BIT (h4/arithmetic/_2B l n) a)
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_Q202645,TV_Q202641]: ![V_f, V_g]: (![V_x]: s(TV_Q202641,happ(s(t_fun(TV_Q202645,TV_Q202641),V_f),s(TV_Q202645,V_x))) = s(TV_Q202641,happ(s(t_fun(TV_Q202645,TV_Q202641),V_g),s(TV_Q202645,V_x))) => s(t_fun(TV_Q202645,TV_Q202641),V_f) = s(t_fun(TV_Q202645,TV_Q202641),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> 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_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_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_bits_BITu_u_def, axiom, ![V_n, V_b]: (p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n)))) <=> s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))).
fof(ah4s_bits_BITSu_u_COMPu_u_THM, axiom, ![V_n, V_l2, V_l1, V_h2, V_h1]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_h2),s(t_h4s_nums_num,V_l1))),s(t_h4s_nums_num,V_h1)))) => s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h2),s(t_h4s_nums_num,V_l2),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h1),s(t_h4s_nums_num,V_l1),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_h2),s(t_h4s_nums_num,V_l1))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l2),s(t_h4s_nums_num,V_l1))),s(t_h4s_nums_num,V_n))))).
fof(ch4s_bits_BITu_u_OFu_u_BITSu_u_THM, conjecture, ![V_n, V_l, V_h, V_a]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_h)))) => s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_a))))) = s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_a))))).
