%   ORIGINAL: h4/bitstring/word__concat__v2w
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/arithmetic/MIN__DEF: !n m. h4/arithmetic/MIN m n = h4/bool/COND (h4/prim__rec/_3C m n) m n
% Assm: h4/fcp/index__sum: h4/fcp/dimindex h4/bool/the__value = h4/bool/COND (h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV) (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/words/word__concat__def: !w v. h4/words/word__concat v w = h4/words/w2w (h4/words/word__join v w)
% Assm: h4/bitstring/w2w__v2w: !v. h4/words/w2w (h4/bitstring/v2w v) = h4/bitstring/v2w (h4/bitstring/fixwidth (h4/bool/COND (h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) v)
% Assm: h4/bitstring/word__join__v2w: !v2 v1. h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV ==> h4/words/word__join (h4/bitstring/v2w v1) (h4/bitstring/v2w v2) = h4/bitstring/v2w (h4/list/APPEND v1 (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v2))
% Goal: !v2 v1. h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV ==> h4/words/word__concat (h4/bitstring/v2w v1) (h4/bitstring/v2w v2) = h4/bitstring/v2w (h4/bitstring/fixwidth (h4/arithmetic/MIN (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value))) (h4/list/APPEND v1 (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v2)))
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_arithmetics_MINu_u_DEF]: !n m. h4/arithmetic/MIN m n = h4/bool/COND (h4/prim__rec/_3C m n) m n
% Assm [h4s_fcps_indexu_u_sum]: ?v. (v <=> h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV) /\ h4/fcp/dimindex h4/bool/the__value = h4/bool/COND v (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_wordss_wordu_u_concatu_u_def]: !w v. h4/words/word__concat v w = h4/words/w2w (h4/words/word__join v w)
% Assm [h4s_bitstrings_w2wu_u_v2w]: !v. h4/words/w2w (h4/bitstring/v2w v) = h4/bitstring/v2w (h4/bitstring/fixwidth (h4/bool/COND (h4/prim__rec/_3C (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value)) v)
% Assm [h4s_bitstrings_wordu_u_joinu_u_v2w]: !v2 v1. h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV ==> h4/words/word__join (h4/bitstring/v2w v1) (h4/bitstring/v2w v2) = h4/bitstring/v2w (h4/list/APPEND v1 (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v2))
% Goal: !v2 v1. h4/pred__set/FINITE h4/pred__set/UNIV /\ h4/pred__set/FINITE h4/pred__set/UNIV ==> h4/words/word__concat (h4/bitstring/v2w v1) (h4/bitstring/v2w v2) = h4/bitstring/v2w (h4/bitstring/fixwidth (h4/arithmetic/MIN (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/_2B (h4/fcp/dimindex h4/bool/the__value) (h4/fcp/dimindex h4/bool/the__value))) (h4/list/APPEND v1 (h4/bitstring/fixwidth (h4/fcp/dimindex h4/bool/the__value) v2)))
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_Q89582,TV_Q89578]: ![V_f, V_g]: (![V_x]: s(TV_Q89578,happ(s(t_fun(TV_Q89582,TV_Q89578),V_f),s(TV_Q89582,V_x))) = s(TV_Q89578,happ(s(t_fun(TV_Q89582,TV_Q89578),V_g),s(TV_Q89582,V_x))) => s(t_fun(TV_Q89582,TV_Q89578),V_f) = s(t_fun(TV_Q89582,TV_Q89578),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> 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_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_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_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_arithmetics_MINu_u_DEF, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_fcps_indexu_u_sum, axiom, ![TV_u_27a,TV_u_27b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)))) & p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_univ)))))) & s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),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))))))))).
fof(ah4s_wordss_wordu_u_concatu_u_def, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_wordss_wordu_u_concat(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_join(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_w)))))).
fof(ah4s_bitstrings_w2wu_u_v2w, axiom, ![TV_u_27b,TV_u_27a]: ![V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_w2w(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))),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)))))).
fof(ah4s_bitstrings_wordu_u_joinu_u_v2w, axiom, ![TV_u_27a,TV_u_27b]: ![V_v2, V_v1]: ((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)))) & p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_univ))))) => s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_wordss_wordu_u_join(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v1))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v2))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),V_v1),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_27b),h4s_bools_theu_u_value))),s(t_h4s_lists_list(t_bool),V_v2))))))))).
fof(ch4s_bitstrings_wordu_u_concatu_u_v2w, conjecture, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_v2, V_v1]: ((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)))) & p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_univ))))) => s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_wordss_wordu_u_concat(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v1))),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),V_v2))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27c),h4s_bitstrings_v2w(s(t_h4s_lists_list(t_bool),h4s_bitstrings_fixwidth(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27c),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))))),s(t_h4s_lists_list(t_bool),h4s_lists_append(s(t_h4s_lists_list(t_bool),V_v1),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_27b),h4s_bools_theu_u_value))),s(t_h4s_lists_list(t_bool),V_v2))))))))))).
