%   ORIGINAL: h4/seq/SEQ__LE
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/LESS__EQ__REFL: !m. h4/arithmetic/_3C_3D m m
% Assm: h4/arithmetic/GREATER__EQ: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm: h4/nets/DORDER__NGE: h4/nets/dorder h4/arithmetic/_3E_3D
% Assm: h4/nets/NET__LE: !g. h4/nets/dorder g ==> (!x x0 y y0. h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) g) /\ h4/nets/tends y y0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) g) /\ (?N. g N N /\ (!n. g n N ==> h4/real/real__lte (x n) (y n))) ==> h4/real/real__lte x0 y0)
% Assm: h4/seq/tends__num__real: !x0 x. h4/seq/_2D_2D_3E x x0 <=> h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) h4/arithmetic/_3E_3D)
% Goal: !m l g f. h4/seq/_2D_2D_3E f l /\ h4/seq/_2D_2D_3E g m /\ (?N. !n. h4/arithmetic/_3E_3D n N ==> h4/real/real__lte (f n) (g n)) ==> h4/real/real__lte l m
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_LESSu_u_EQu_u_REFL]: !m. h4/arithmetic/_3C_3D m m
% Assm [h4s_arithmetics_GREATERu_u_EQ]: !n m. happ (happ h4/arithmetic/_3E_3D n) m <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_netss_DORDERu_u_NGE]: h4/nets/dorder h4/arithmetic/_3E_3D
% Assm [h4s_netss_NETu_u_LE]: !g. h4/nets/dorder g ==> (!x x0 y y0. h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) g) /\ h4/nets/tends y y0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) g) /\ (?N. happ (happ g N) N /\ (!n. happ (happ g n) N ==> h4/real/real__lte (happ x n) (happ y n))) ==> h4/real/real__lte x0 y0)
% Assm [h4s_seqs_tendsu_u_numu_u_real]: !x0 x. h4/seq/_2D_2D_3E x x0 <=> h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) h4/arithmetic/_3E_3D)
% Goal: !m l g f. h4/seq/_2D_2D_3E f l /\ h4/seq/_2D_2D_3E g m /\ (?N. !n. happ (happ h4/arithmetic/_3E_3D n) N ==> h4/real/real__lte (happ f n) (happ g n)) ==> h4/real/real__lte l m
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q133558,TV_Q133554]: ![V_f, V_g]: (![V_x]: s(TV_Q133554,happ(s(t_fun(TV_Q133558,TV_Q133554),V_f),s(TV_Q133558,V_x))) = s(TV_Q133554,happ(s(t_fun(TV_Q133558,TV_Q133554),V_g),s(TV_Q133558,V_x))) => s(t_fun(TV_Q133558,TV_Q133554),V_f) = s(t_fun(TV_Q133558,TV_Q133554),V_g))).
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_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_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_LESSu_u_EQu_u_REFL, axiom, ![V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_m))))).
fof(ah4s_arithmetics_GREATERu_u_EQ, axiom, ![V_n, V_m]: 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)),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_netss_DORDERu_u_NGE, axiom, p(s(t_bool,h4s_netss_dorder(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d))))).
fof(ah4s_netss_NETu_u_LE, axiom, ![TV_u_27a]: ![V_g]: (p(s(t_bool,h4s_netss_dorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_g)))) => ![V_x, V_x0, V_y, V_y0]: ((p(s(t_bool,h4s_netss_tends(s(t_fun(TV_u_27a,t_h4s_realaxs_real),V_x),s(t_h4s_realaxs_real,V_x0),s(t_h4s_pairs_prod(t_h4s_topologys_topology(t_h4s_realaxs_real),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_topology(t_h4s_realaxs_real),h4s_topologys_mtop(s(t_h4s_topologys_metric(t_h4s_realaxs_real),h4s_topologys_mr1))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_g)))))) & (p(s(t_bool,h4s_netss_tends(s(t_fun(TV_u_27a,t_h4s_realaxs_real),V_y),s(t_h4s_realaxs_real,V_y0),s(t_h4s_pairs_prod(t_h4s_topologys_topology(t_h4s_realaxs_real),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_topology(t_h4s_realaxs_real),h4s_topologys_mtop(s(t_h4s_topologys_metric(t_h4s_realaxs_real),h4s_topologys_mr1))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_g)))))) & ?[V_N]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_g),s(TV_u_27a,V_N))),s(TV_u_27a,V_N)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_g),s(TV_u_27a,V_n))),s(TV_u_27a,V_N)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(TV_u_27a,t_h4s_realaxs_real),V_x),s(TV_u_27a,V_n))),s(t_h4s_realaxs_real,happ(s(t_fun(TV_u_27a,t_h4s_realaxs_real),V_y),s(TV_u_27a,V_n)))))))))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x0),s(t_h4s_realaxs_real,V_y0))))))).
fof(ah4s_seqs_tendsu_u_numu_u_real, axiom, ![V_x0, V_x]: s(t_bool,h4s_seqs_u_2du_2du_3e(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_x),s(t_h4s_realaxs_real,V_x0))) = s(t_bool,h4s_netss_tends(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_x),s(t_h4s_realaxs_real,V_x0),s(t_h4s_pairs_prod(t_h4s_topologys_topology(t_h4s_realaxs_real),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_topology(t_h4s_realaxs_real),h4s_topologys_mtop(s(t_h4s_topologys_metric(t_h4s_realaxs_real),h4s_topologys_mr1))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3eu_3d)))))).
fof(ch4s_seqs_SEQu_u_LE, conjecture, ![V_m, V_l, V_g, V_f]: ((p(s(t_bool,h4s_seqs_u_2du_2du_3e(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l)))) & (p(s(t_bool,h4s_seqs_u_2du_2du_3e(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_m)))) & ?[V_N]: ![V_n]: (p(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)),h4s_arithmetics_u_3eu_3d),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_N)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f),s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_g),s(t_h4s_nums_num,V_n))))))))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_m)))))).
