%   ORIGINAL: h4/bit/BITS__SLICE__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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/MULT__DIV: !q n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/DIV (h4/arithmetic/_2A q n) n = q
% Assm: h4/bit/ZERO__LT__TWOEXP: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)
% Assm: h4/bit/BITS__LT__HIGH: !n l h. h4/prim__rec/_3C n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h)) ==> h4/bit/BITS h l n = h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)
% Assm: h4/bit/SLICE__THM: !n l h. h4/bit/SLICE h l n = h4/arithmetic/_2A (h4/bit/BITS h l n) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)
% Assm: h4/bit/SLICELT__THM: !n l h. h4/prim__rec/_3C (h4/bit/SLICE h l n) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h))
% Goal: !n l h. h4/bit/BITS h l (h4/bit/SLICE h l n) = h4/bit/BITS h l 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_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_MULTu_u_DIV]: !q n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/DIV (h4/arithmetic/_2A q n) n = q
% Assm [h4s_bits_ZEROu_u_LTu_u_TWOEXP]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)
% Assm [h4s_bits_BITSu_u_LTu_u_HIGH]: !n l h. h4/prim__rec/_3C n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h)) ==> h4/bit/BITS h l n = h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)
% Assm [h4s_bits_SLICEu_u_THM]: !n l h. h4/bit/SLICE h l n = h4/arithmetic/_2A (h4/bit/BITS h l n) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)
% Assm [h4s_bits_SLICELTu_u_THM]: !n l h. h4/prim__rec/_3C (h4/bit/SLICE h l n) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h))
% Goal: !n l h. h4/bit/BITS h l (h4/bit/SLICE h l n) = h4/bit/BITS h l 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_Q201590,TV_Q201586]: ![V_f, V_g]: (![V_x]: s(TV_Q201586,happ(s(t_fun(TV_Q201590,TV_Q201586),V_f),s(TV_Q201590,V_x))) = s(TV_Q201586,happ(s(t_fun(TV_Q201590,TV_Q201586),V_g),s(TV_Q201590,V_x))) => s(t_fun(TV_Q201590,TV_Q201586),V_f) = s(t_fun(TV_Q201590,TV_Q201586),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_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_arithmetics_MULTu_u_DIV, axiom, ![V_q, V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_q),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,V_q))).
fof(ah4s_bits_ZEROu_u_LTu_u_TWOEXP, axiom, ![V_n]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),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_n))))))).
fof(ah4s_bits_BITSu_u_LTu_u_HIGH, axiom, ![V_n, V_l, V_h]: (p(s(t_bool,h4s_primu_u_recs_u_3c(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,h4s_nums_suc(s(t_h4s_nums_num,V_h)))))))) => 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_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_l))))))).
fof(ah4s_bits_SLICEu_u_THM, axiom, ![V_n, V_l, V_h]: s(t_h4s_nums_num,h4s_bits_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(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_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_l)))))).
fof(ah4s_bits_SLICELTu_u_THM, axiom, ![V_n, V_l, V_h]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_bits_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),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,h4s_nums_suc(s(t_h4s_nums_num,V_h))))))))).
fof(ch4s_bits_BITSu_u_SLICEu_u_THM, conjecture, ![V_n, V_l, V_h]: 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,h4s_bits_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),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_n)))).
