%   ORIGINAL: h4/bitstring/ranged__bitstring__nchotomy
% 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/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/bitstring/length__fixwidth: !v n. h4/list/LENGTH (h4/bitstring/fixwidth n v) = n
% Assm: h4/bitstring/v2w__fixwidth: !v. h4/bitstring/v2w (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v) = h4/bitstring/v2w v
% Assm: h4/bitstring/bitstring__nchotomy: !w. ?v. w = h4/bitstring/v2w v
% Goal: !w. ?v. w = h4/bitstring/v2w v /\ h4/marker/Abbrev (h4/list/LENGTH v = h4/fcp/dimindex h4/bool/the__value)
%   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_markers_Abbrevu_u_def]: !x. h4/marker/Abbrev x <=> x
% Assm [h4s_bitstrings_lengthu_u_fixwidth]: !v n. h4/list/LENGTH (h4/bitstring/fixwidth n v) = n
% Assm [h4s_bitstrings_v2wu_u_fixwidth]: !v. h4/bitstring/v2w (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v) = h4/bitstring/v2w v
% Assm [h4s_bitstrings_bitstringu_u_nchotomy]: !w. ?v. w = h4/bitstring/v2w v
% Goal: !w. ?v. w = h4/bitstring/v2w v /\ (?v. (v <=> h4/list/LENGTH v = h4/fcp/dimindex h4/bool/the__value) /\ h4/marker/Abbrev v)
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_Q88735,TV_Q88731]: ![V_f, V_g]: (![V_x]: s(TV_Q88731,happ(s(t_fun(TV_Q88735,TV_Q88731),V_f),s(TV_Q88735,V_x))) = s(TV_Q88731,happ(s(t_fun(TV_Q88735,TV_Q88731),V_g),s(TV_Q88735,V_x))) => s(t_fun(TV_Q88735,TV_Q88731),V_f) = s(t_fun(TV_Q88735,TV_Q88731),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_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_bitstrings_lengthu_u_fixwidth, axiom, ![V_v, V_n]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_bitstrings_v2wu_u_fixwidth, axiom, ![TV_u_27a]: ![V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v)))).
fof(ah4s_bitstrings_bitstringu_u_nchotomy, axiom, ![TV_u_27a]: ![V_w]: ?[V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v)))).
fof(ch4s_bitstrings_rangedu_u_bitstringu_u_nchotomy, conjecture, ![TV_u_27a]: ![V_w]: ?[V_v]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))) & ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_bool),V_v))) = s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))) & p(s(t_bool,h4s_markers_abbrev(s(t_bool,V_v0))))))).
