%   ORIGINAL: h4/words/WORD__GE
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/arithmetic/GREATER__EQ: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm: h4/words/WORD__GREATER__EQ: !b a. h4/words/word__ge a b <=> h4/words/word__le b a
% Assm: h4/words/WORD__LE: !b a. h4/words/word__le a b <=> (h4/words/word__msb a <=> h4/words/word__msb b) /\ h4/arithmetic/_3C_3D (h4/words/w2n a) (h4/words/w2n b) \/ h4/words/word__msb a /\ ~h4/words/word__msb b
% Goal: !b a. h4/words/word__ge a b <=> (h4/words/word__msb b <=> h4/words/word__msb a) /\ h4/arithmetic/_3E_3D (h4/words/w2n a) (h4/words/w2n b) \/ h4/words/word__msb b /\ ~h4/words/word__msb a
%   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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_arithmetics_GREATERu_u_EQ]: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_wordss_WORDu_u_GREATERu_u_EQ]: !b a. h4/words/word__ge a b <=> h4/words/word__le b a
% Assm [h4s_wordss_WORDu_u_LE]: !b a. h4/words/word__le a b <=> (h4/words/word__msb a <=> h4/words/word__msb b) /\ h4/arithmetic/_3C_3D (h4/words/w2n a) (h4/words/w2n b) \/ h4/words/word__msb a /\ ~h4/words/word__msb b
% Goal: !b a. h4/words/word__ge a b <=> (h4/words/word__msb b <=> h4/words/word__msb a) /\ h4/arithmetic/_3E_3D (h4/words/w2n a) (h4/words/w2n b) \/ h4/words/word__msb b /\ ~h4/words/word__msb a
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_Q126551,TV_Q126547]: ![V_f, V_g]: (![V_x]: s(TV_Q126547,happ(s(t_fun(TV_Q126551,TV_Q126547),V_f),s(TV_Q126551,V_x))) = s(TV_Q126547,happ(s(t_fun(TV_Q126551,TV_Q126547),V_g),s(TV_Q126551,V_x))) => s(t_fun(TV_Q126551,TV_Q126547),V_f) = s(t_fun(TV_Q126551,TV_Q126547),V_g))).
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_arithmetics_GREATERu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_wordss_WORDu_u_GREATERu_u_EQ, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_ge(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
fof(ah4s_wordss_WORDu_u_LE, axiom, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_le(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) <=> ((s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))))) | (p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))) & ~ (p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))))))).
fof(ch4s_wordss_WORDu_u_GE, conjecture, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_ge(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) <=> ((s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) & p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))))) | (p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & ~ (p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))))))))).
