%   ORIGINAL: h4/words/EXTRACT__JOIN__LSL
% 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/AND__CLAUSES_c0: !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/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/words/EXTRACT__JOIN: !w s m_27 m l h. h4/arithmetic/_3C_3D l m /\ h4/arithmetic/_3C_3D m_27 h /\ m_27 = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ s = h4/arithmetic/_2D m_27 l ==> h4/words/word__or (h4/words/word__lsl (h4/words/word__extract h m_27 w) s) (h4/words/word__extract m l w) = h4/words/word__extract (h4/arithmetic/MIN h (h4/arithmetic/MIN (h4/arithmetic/_2D (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) l w
% Assm: h4/words/LSL__ADD: !w n m. h4/words/word__lsl (h4/words/word__lsl w m) n = h4/words/word__lsl w (h4/arithmetic/_2B m n)
% Assm: h4/words/LSL__BITWISE_c1: !w v n. h4/words/word__or (h4/words/word__lsl w n) (h4/words/word__lsl v n) = h4/words/word__lsl (h4/words/word__or w v) n
% Goal: !w s n m_27 m l h. h4/arithmetic/_3C_3D l m /\ h4/arithmetic/_3C_3D m_27 h /\ m_27 = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ s = h4/arithmetic/_2B (h4/arithmetic/_2D m_27 l) n ==> h4/words/word__or (h4/words/word__lsl (h4/words/word__extract h m_27 w) s) (h4/words/word__lsl (h4/words/word__extract m l w) n) = h4/words/word__lsl (h4/words/word__extract (h4/arithmetic/MIN h (h4/arithmetic/MIN (h4/arithmetic/_2D (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) l w) 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_ANDu_u_CLAUSESu_c0]: !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_markers_Abbrevu_u_def]: !x. h4/marker/Abbrev x <=> x
% Assm [h4s_wordss_EXTRACTu_u_JOIN]: !w s m_27 m l h. h4/arithmetic/_3C_3D l m /\ h4/arithmetic/_3C_3D m_27 h /\ m_27 = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ s = h4/arithmetic/_2D m_27 l ==> h4/words/word__or (h4/words/word__lsl (h4/words/word__extract h m_27 w) s) (h4/words/word__extract m l w) = h4/words/word__extract (h4/arithmetic/MIN h (h4/arithmetic/MIN (h4/arithmetic/_2D (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) l w
% Assm [h4s_wordss_LSLu_u_ADD]: !w n m. h4/words/word__lsl (h4/words/word__lsl w m) n = h4/words/word__lsl w (h4/arithmetic/_2B m n)
% Assm [h4s_wordss_LSLu_u_BITWISEu_c1]: !w v n. h4/words/word__or (h4/words/word__lsl w n) (h4/words/word__lsl v n) = h4/words/word__lsl (h4/words/word__or w v) n
% Goal: !w s n m_27 m l h. h4/arithmetic/_3C_3D l m /\ h4/arithmetic/_3C_3D m_27 h /\ m_27 = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) /\ s = h4/arithmetic/_2B (h4/arithmetic/_2D m_27 l) n ==> h4/words/word__or (h4/words/word__lsl (h4/words/word__extract h m_27 w) s) (h4/words/word__lsl (h4/words/word__extract m l w) n) = h4/words/word__lsl (h4/words/word__extract (h4/arithmetic/MIN h (h4/arithmetic/MIN (h4/arithmetic/_2D (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) l) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) l w) 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_Q125884,TV_Q125880]: ![V_f, V_g]: (![V_x]: s(TV_Q125880,happ(s(t_fun(TV_Q125884,TV_Q125880),V_f),s(TV_Q125884,V_x))) = s(TV_Q125880,happ(s(t_fun(TV_Q125884,TV_Q125880),V_g),s(TV_Q125884,V_x))) => s(t_fun(TV_Q125884,TV_Q125880),V_f) = s(t_fun(TV_Q125884,TV_Q125880),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_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_markers_Abbrevu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_abbrev(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_wordss_EXTRACTu_u_JOIN, axiom, ![TV_u_27b,TV_u_27a]: ![V_w, V_s, V_mu_27, V_m, V_l, V_h]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_m)))) & (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_mu_27),s(t_h4s_nums_num,V_h)))) & (s(t_h4s_nums_num,V_mu_27) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),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_s) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_mu_27),s(t_h4s_nums_num,V_l)))))) => s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_mu_27),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_s))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),s(t_h4s_nums_num,V_l))),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_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))).
fof(ah4s_wordss_LSLu_u_ADD, axiom, ![TV_u_27a]: ![V_w, V_n, V_m]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_wordss_LSLu_u_BITWISEu_c1, axiom, ![TV_u_27a]: ![V_w, V_v, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_n))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_nums_num,V_n)))).
fof(ch4s_wordss_EXTRACTu_u_JOINu_u_LSL, conjecture, ![TV_u_27b,TV_u_27a]: ![V_w, V_s, V_n, V_mu_27, V_m, V_l, V_h]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_m)))) & (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_mu_27),s(t_h4s_nums_num,V_h)))) & (s(t_h4s_nums_num,V_mu_27) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),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_s) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_mu_27),s(t_h4s_nums_num,V_l))),s(t_h4s_nums_num,V_n)))))) => s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_mu_27),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_s))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_lsl(s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),s(t_h4s_nums_num,V_l))),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_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))).
