%   ORIGINAL: h4/bitstring/length__shiftr
% 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/SUB__LESS__EQ: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D n m) n
% Assm: h4/list/LENGTH__TAKE: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/list/LENGTH (h4/list/TAKE n l) = n
% Assm: h4/bitstring/shiftr__def: !v m. h4/bitstring/shiftr v m = h4/list/TAKE (h4/arithmetic/_2D (h4/list/LENGTH v) m) v
% Goal: !v n. h4/list/LENGTH (h4/bitstring/shiftr v n) = h4/arithmetic/_2D (h4/list/LENGTH 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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_SUBu_u_LESSu_u_EQ]: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D n m) n
% Assm [h4s_lists_LENGTHu_u_TAKE]: !n l. h4/arithmetic/_3C_3D n (h4/list/LENGTH l) ==> h4/list/LENGTH (h4/list/TAKE n l) = n
% Assm [h4s_bitstrings_shiftru_u_def]: !v m. h4/bitstring/shiftr v m = h4/list/TAKE (h4/arithmetic/_2D (h4/list/LENGTH v) m) v
% Goal: !v n. h4/list/LENGTH (h4/bitstring/shiftr v n) = h4/arithmetic/_2D (h4/list/LENGTH 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_Q88154,TV_Q88150]: ![V_f, V_g]: (![V_x]: s(TV_Q88150,happ(s(t_fun(TV_Q88154,TV_Q88150),V_f),s(TV_Q88154,V_x))) = s(TV_Q88150,happ(s(t_fun(TV_Q88154,TV_Q88150),V_g),s(TV_Q88154,V_x))) => s(t_fun(TV_Q88154,TV_Q88150),V_f) = s(t_fun(TV_Q88154,TV_Q88150),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_SUBu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))).
fof(ah4s_lists_LENGTHu_u_TAKE, axiom, ![TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_take(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,V_n))).
fof(ah4s_bitstrings_shiftru_u_def, axiom, ![TV_u_27a]: ![V_v, V_m]: s(t_h4s_lists_list(TV_u_27a),h4s_bitstrings_shiftr(s(t_h4s_lists_list(TV_u_27a),V_v),s(t_h4s_nums_num,V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_take(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_v))),s(t_h4s_nums_num,V_m))),s(t_h4s_lists_list(TV_u_27a),V_v)))).
fof(ch4s_bitstrings_lengthu_u_shiftr, conjecture, ![TV_u_27a]: ![V_v, V_n]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_bitstrings_shiftr(s(t_h4s_lists_list(TV_u_27a),V_v),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_v))),s(t_h4s_nums_num,V_n)))).
