%   ORIGINAL: h4/nets/NET__CONV__BOUNDED
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> 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/prim__rec/LESS__0: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/real/REAL__LT: !n m. h4/realax/real__lt (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/prim__rec/_3C m n
% Assm: h4/nets/bounded0: !m g f. h4/nets/bounded (h4/pair/_2C m g) f <=> (?k x N. g N N /\ (!n. g n N ==> h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C (f n) x)) k))
% Assm: h4/nets/MTOP__TENDS: !x0 x g d. h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop d) g) <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?n. g n n /\ (!m. g m n ==> h4/realax/real__lt (h4/topology/dist d (h4/pair/_2C (x m) x0)) e)))
% Goal: !x0 x g. h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) g) ==> h4/nets/bounded (h4/pair/_2C h4/topology/mr1 g) x
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> 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_primu_u_recs_LESSu_u_0]: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_reals_REALu_u_LT]: !n m. h4/realax/real__lt (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/prim__rec/_3C m n
% Assm [h4s_netss_bounded0]: !m g f. h4/nets/bounded (h4/pair/_2C m g) f <=> (?k x N. happ (happ g N) N /\ (!n. happ (happ g n) N ==> h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C (happ f n) x)) k))
% Assm [h4s_netss_MTOPu_u_TENDS]: !x0 x g d. h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop d) g) <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?n. happ (happ g n) n /\ (!m. happ (happ g m) n ==> h4/realax/real__lt (h4/topology/dist d (h4/pair/_2C (happ x m) x0)) e)))
% Goal: !x0 x g. h4/nets/tends x x0 (h4/pair/_2C (h4/topology/mtop h4/topology/mr1) g) ==> h4/nets/bounded (h4/pair/_2C h4/topology/mr1 g) x
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_Q198847,TV_Q198843]: ![V_f, V_g]: (![V_x]: s(TV_Q198843,happ(s(t_fun(TV_Q198847,TV_Q198843),V_f),s(TV_Q198847,V_x))) = s(TV_Q198843,happ(s(t_fun(TV_Q198847,TV_Q198843),V_g),s(TV_Q198847,V_x))) => s(t_fun(TV_Q198847,TV_Q198843),V_f) = s(t_fun(TV_Q198847,TV_Q198843),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_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_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_primu_u_recs_LESSu_u_0, axiom, ![V_n]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))).
fof(ah4s_arithmetics_ONE, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_reals_REALu_u_LT, axiom, ![V_n, V_m]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_netss_bounded0, axiom, ![TV_u_27b,TV_u_27a]: ![V_m, V_g, V_f]: (p(s(t_bool,h4s_netss_bounded(s(t_h4s_pairs_prod(t_h4s_topologys_metric(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_g))),s(t_fun(TV_u_27b,TV_u_27a),V_f)))) <=> ?[V_k, V_x, V_N]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_g),s(TV_u_27b,V_N))),s(TV_u_27b,V_N)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_g),s(TV_u_27b,V_n))),s(TV_u_27b,V_N)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(TV_u_27b,V_n))),s(TV_u_27a,V_x))))),s(t_h4s_realaxs_real,V_k)))))))).
fof(ah4s_netss_MTOPu_u_TENDS, axiom, ![TV_u_27b,TV_u_27a]: ![V_x0, V_x, V_g, V_d]: (p(s(t_bool,h4s_netss_tends(s(t_fun(TV_u_27b,TV_u_27a),V_x),s(TV_u_27a,V_x0),s(t_h4s_pairs_prod(t_h4s_topologys_topology(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool))),h4s_pairs_u_2c(s(t_h4s_topologys_topology(TV_u_27a),h4s_topologys_mtop(s(t_h4s_topologys_metric(TV_u_27a),V_d))),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_g)))))) <=> ![V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) => ?[V_n]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_g),s(TV_u_27b,V_n))),s(TV_u_27b,V_n)))) & ![V_m]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_g),s(TV_u_27b,V_m))),s(TV_u_27b,V_n)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_d),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x),s(TV_u_27b,V_m))),s(TV_u_27a,V_x0))))),s(t_h4s_realaxs_real,V_e))))))))).
fof(ch4s_netss_NETu_u_CONVu_u_BOUNDED, conjecture, ![TV_u_27a]: ![V_x0, V_x, V_g]: (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_bounded(s(t_h4s_pairs_prod(t_h4s_topologys_metric(t_h4s_realaxs_real),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_pairs_u_2c(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))),s(t_fun(TV_u_27a,t_h4s_realaxs_real),V_x)))))).
