%   ORIGINAL: h4/words/word__lsb__n2w
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bit/BIT0__ODD: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm: h4/fcp/FCP__BETA: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = g i
% Assm: h4/words/n2w__def: !n. h4/words/n2w n = h4/fcp/FCP (\i. h4/bit/BIT i n)
% Assm: h4/words/word__lsb__def: !w. h4/words/word__lsb w <=> h4/fcp/fcp__index w h4/num/0
% Assm: h4/words/DIMINDEX__GT__0: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Goal: !n. h4/words/word__lsb (h4/words/n2w n) <=> h4/arithmetic/ODD 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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bits_BIT0u_u_ODD]: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm [h4s_fcps_FCPu_u_BETA]: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = happ g i
% Assm [h4s_wordss_n2wu_u_def]: !_0. (!n i. happ (happ _0 n) i <=> happ (h4/bit/BIT i) n) ==> (!n. h4/words/n2w n = h4/fcp/FCP (happ _0 n))
% Assm [h4s_wordss_wordu_u_lsbu_u_def]: !w. h4/words/word__lsb w <=> h4/fcp/fcp__index w h4/num/0
% Assm [h4s_wordss_DIMINDEXu_u_GTu_u_0]: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Goal: !n. h4/words/word__lsb (h4/words/n2w n) <=> happ h4/arithmetic/ODD 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_Q117508,TV_Q117504]: ![V_f, V_g]: (![V_x]: s(TV_Q117504,happ(s(t_fun(TV_Q117508,TV_Q117504),V_f),s(TV_Q117508,V_x))) = s(TV_Q117504,happ(s(t_fun(TV_Q117508,TV_Q117504),V_g),s(TV_Q117508,V_x))) => s(t_fun(TV_Q117508,TV_Q117504),V_f) = s(t_fun(TV_Q117508,TV_Q117504),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_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_bits_BIT0u_u_ODD, axiom, s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_0))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd)).
fof(ah4s_fcps_FCPu_u_BETA, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_g]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,V_i))))).
fof(ah4s_wordss_n2wu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_n))) => ![V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_wordu_u_lsbu_u_def, axiom, ![TV_u_27a]: ![V_w]: s(t_bool,h4s_wordss_wordu_u_lsb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_wordss_DIMINDEXu_u_GTu_u_0, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ch4s_wordss_wordu_u_lsbu_u_n2w, conjecture, ![TV_u_27a]: ![V_n]: s(t_bool,h4s_wordss_wordu_u_lsb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd),s(t_h4s_nums_num,V_n)))).
