%   ORIGINAL: h4/words/ROL__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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/words/word__rol__def: !w n. h4/words/word__rol w n = h4/words/word__ror w (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/MOD n (h4/fcp/dimindex h4/bool/the__value)))
% Assm: h4/words/ROR__BITWISE_c0: !w v n. h4/words/word__and (h4/words/word__ror w n) (h4/words/word__ror v n) = h4/words/word__ror (h4/words/word__and w v) n
% Goal: !w v n. h4/words/word__and (h4/words/word__rol w n) (h4/words/word__rol v n) = h4/words/word__rol (h4/words/word__and w v) 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_wordss_wordu_u_rolu_u_def]: !w n. h4/words/word__rol w n = h4/words/word__ror w (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/MOD n (h4/fcp/dimindex h4/bool/the__value)))
% Assm [h4s_wordss_RORu_u_BITWISEu_c0]: !w v n. h4/words/word__and (h4/words/word__ror w n) (h4/words/word__ror v n) = h4/words/word__ror (h4/words/word__and w v) n
% Goal: !w v n. h4/words/word__and (h4/words/word__rol w n) (h4/words/word__rol v n) = h4/words/word__rol (h4/words/word__and w v) 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_Q125659,TV_Q125655]: ![V_f, V_g]: (![V_x]: s(TV_Q125655,happ(s(t_fun(TV_Q125659,TV_Q125655),V_f),s(TV_Q125659,V_x))) = s(TV_Q125655,happ(s(t_fun(TV_Q125659,TV_Q125655),V_g),s(TV_Q125659,V_x))) => s(t_fun(TV_Q125659,TV_Q125655),V_f) = s(t_fun(TV_Q125659,TV_Q125655),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_wordss_wordu_u_rolu_u_def, axiom, ![TV_u_27a]: ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_rol(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_ror(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),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_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))))).
fof(ah4s_wordss_RORu_u_BITWISEu_c0, axiom, ![TV_u_27a]: ![V_w, V_v, V_n]: 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),h4s_wordss_wordu_u_ror(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_ror(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_ror(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_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_nums_num,V_n)))).
fof(ch4s_wordss_ROLu_u_BITWISEu_c0, conjecture, ![TV_u_27a]: ![V_w, V_v, V_n]: 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),h4s_wordss_wordu_u_rol(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_rol(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_rol(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_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_nums_num,V_n)))).
