%   ORIGINAL: h4/seq/SUM__SUMMABLE
% 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/seq/summable0: !f. h4/seq/summable f <=> (?s. h4/seq/sums f s)
% Goal: !l f. h4/seq/sums f l ==> h4/seq/summable f
%   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_seqs_summable0]: !f. h4/seq/summable f <=> (?s. h4/seq/sums f s)
% Goal: !l f. h4/seq/sums f l ==> h4/seq/summable f
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_Q133808,TV_Q133804]: ![V_f, V_g]: (![V_x]: s(TV_Q133804,happ(s(t_fun(TV_Q133808,TV_Q133804),V_f),s(TV_Q133808,V_x))) = s(TV_Q133804,happ(s(t_fun(TV_Q133808,TV_Q133804),V_g),s(TV_Q133808,V_x))) => s(t_fun(TV_Q133808,TV_Q133804),V_f) = s(t_fun(TV_Q133808,TV_Q133804),V_g))).
fof(ah4s_seqs_summable0, axiom, ![V_f]: (p(s(t_bool,h4s_seqs_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f)))) <=> ?[V_s]: p(s(t_bool,h4s_seqs_sums(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_s)))))).
fof(ch4s_seqs_SUMu_u_SUMMABLE, conjecture, ![V_l, V_f]: (p(s(t_bool,h4s_seqs_sums(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_summable(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f)))))).
