%   ORIGINAL: h4/words/WORD__EXTRACT__OVER__BITWISE_c0
% 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/FORALL__SIMP: !t. (!x. t) <=> 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/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/words/word__extract__def: !l h. h4/words/word__extract h l = h4/combin/o h4/words/w2w (h4/words/word__bits h l)
% Assm: h4/words/WORD__BITS__OVER__BITWISE_c0: !w v l h. h4/words/word__and (h4/words/word__bits h l v) (h4/words/word__bits h l w) = h4/words/word__bits h l (h4/words/word__and v w)
% Assm: h4/words/WORD__BITS__OVER__BITWISE_c1: !w v l h. h4/words/word__or (h4/words/word__bits h l v) (h4/words/word__bits h l w) = h4/words/word__bits h l (h4/words/word__or v w)
% Assm: h4/words/WORD__BITS__OVER__BITWISE_c2: !w v l h. h4/words/word__xor (h4/words/word__bits h l v) (h4/words/word__bits h l w) = h4/words/word__bits h l (h4/words/word__xor v w)
% Assm: h4/words/WORD__w2w__OVER__BITWISE_c0: !w v. h4/words/word__and (h4/words/w2w v) (h4/words/w2w w) = h4/words/w2w (h4/words/word__and v w)
% Assm: h4/words/WORD__w2w__OVER__BITWISE_c1: !w v. h4/words/word__or (h4/words/w2w v) (h4/words/w2w w) = h4/words/w2w (h4/words/word__or v w)
% Assm: h4/words/WORD__w2w__OVER__BITWISE_c2: !w v. h4/words/word__xor (h4/words/w2w v) (h4/words/w2w w) = h4/words/w2w (h4/words/word__xor v w)
% Goal: !w v l h. h4/words/word__and (h4/words/word__extract h l v) (h4/words/word__extract h l w) = h4/words/word__extract h l (h4/words/word__and v w)
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> 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_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_wordss_wordu_u_extractu_u_def]: !l h. h4/words/word__extract h l = h4/combin/o h4/words/w2w (h4/words/word__bits h l)
% Assm [h4s_wordss_WORDu_u_BITSu_u_OVERu_u_BITWISEu_c0]: !w v l h. h4/words/word__and (happ (h4/words/word__bits h l) v) (happ (h4/words/word__bits h l) w) = happ (h4/words/word__bits h l) (h4/words/word__and v w)
% Assm [h4s_wordss_WORDu_u_BITSu_u_OVERu_u_BITWISEu_c1]: !w v l h. h4/words/word__or (happ (h4/words/word__bits h l) v) (happ (h4/words/word__bits h l) w) = happ (h4/words/word__bits h l) (h4/words/word__or v w)
% Assm [h4s_wordss_WORDu_u_BITSu_u_OVERu_u_BITWISEu_c2]: !w v l h. h4/words/word__xor (happ (h4/words/word__bits h l) v) (happ (h4/words/word__bits h l) w) = happ (h4/words/word__bits h l) (h4/words/word__xor v w)
% Assm [h4s_wordss_WORDu_u_w2wu_u_OVERu_u_BITWISEu_c0]: !w v. h4/words/word__and (happ h4/words/w2w v) (happ h4/words/w2w w) = happ h4/words/w2w (h4/words/word__and v w)
% Assm [h4s_wordss_WORDu_u_w2wu_u_OVERu_u_BITWISEu_c1]: !w v. h4/words/word__or (happ h4/words/w2w v) (happ h4/words/w2w w) = happ h4/words/w2w (h4/words/word__or v w)
% Assm [h4s_wordss_WORDu_u_w2wu_u_OVERu_u_BITWISEu_c2]: !w v. h4/words/word__xor (happ h4/words/w2w v) (happ h4/words/w2w w) = happ h4/words/w2w (h4/words/word__xor v w)
% Goal: !w v l h. h4/words/word__and (happ (h4/words/word__extract h l) v) (happ (h4/words/word__extract h l) w) = happ (h4/words/word__extract h l) (h4/words/word__and v w)
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_Q121347,TV_Q121343]: ![V_f, V_g]: (![V_x]: s(TV_Q121343,happ(s(t_fun(TV_Q121347,TV_Q121343),V_f),s(TV_Q121347,V_x))) = s(TV_Q121343,happ(s(t_fun(TV_Q121347,TV_Q121343),V_g),s(TV_Q121347,V_x))) => s(t_fun(TV_Q121347,TV_Q121343),V_f) = s(t_fun(TV_Q121347,TV_Q121343),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_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_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_wordss_wordu_u_extractu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_h]: s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),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_l))) = s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l)))))).
fof(ah4s_wordss_WORDu_u_BITSu_u_OVERu_u_BITWISEu_c0, axiom, ![TV_u_27a]: ![V_w, V_v, V_l, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),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_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(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_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_BITSu_u_OVERu_u_BITWISEu_c1, axiom, ![TV_u_27a]: ![V_w, V_v, V_l, V_h]: 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),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),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_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(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_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_BITSu_u_OVERu_u_BITWISEu_c2, axiom, ![TV_u_27a]: ![V_w, V_v, V_l, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),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_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(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_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_w2wu_u_OVERu_u_BITWISEu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_w2wu_u_OVERu_u_BITWISEu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_w, V_v]: 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),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),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_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ah4s_wordss_WORDu_u_w2wu_u_OVERu_u_BITWISEu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_xor(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ch4s_wordss_WORDu_u_EXTRACTu_u_OVERu_u_BITWISEu_c0, conjecture, ![TV_u_27b,TV_u_27a]: ![V_w, V_v, V_l, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),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_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),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_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),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_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
