%   ORIGINAL: h4/words/WORD__SLICE__ZERO2
% 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/bit/SLICE__ZERO2: !l h. h4/bit/SLICE h l h4/num/0 = h4/num/0
% Assm: h4/words/word__slice__n2w: !n l h. h4/words/word__slice h l (h4/words/n2w n) = h4/words/n2w (h4/bit/SLICE (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) l n)
% Goal: !l h. h4/words/word__slice h l (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
%   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_bits_SLICEu_u_ZERO2]: !l h. h4/bit/SLICE h l h4/num/0 = h4/num/0
% Assm [h4s_wordss_wordu_u_sliceu_u_n2w]: !n l h. h4/words/word__slice h l (h4/words/n2w n) = h4/words/n2w (h4/bit/SLICE (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) l n)
% Goal: !l h. h4/words/word__slice h l (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
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_Q120720,TV_Q120716]: ![V_f, V_g]: (![V_x]: s(TV_Q120716,happ(s(t_fun(TV_Q120720,TV_Q120716),V_f),s(TV_Q120720,V_x))) = s(TV_Q120716,happ(s(t_fun(TV_Q120720,TV_Q120716),V_g),s(TV_Q120720,V_x))) => s(t_fun(TV_Q120720,TV_Q120716),V_f) = s(t_fun(TV_Q120720,TV_Q120716),V_g))).
fof(ah4s_bits_SLICEu_u_ZERO2, axiom, ![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,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_wordss_wordu_u_sliceu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_l, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_bits_slice(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_h),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_nums_num,V_n)))))).
fof(ch4s_wordss_WORDu_u_SLICEu_u_ZERO2, conjecture, ![TV_u_27a]: ![V_l, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
