%   ORIGINAL: h4/list/LIST__BIND__ID_c1
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/list/MAP__ID_c0: !l. h4/list/MAP (\x. x) l = l
% Assm: h4/list/MAP__ID_c1: !l. h4/list/MAP h4/combin/I l = l
% Assm: h4/list/LIST__BIND__DEF: !l f. h4/list/LIST__BIND l f = h4/list/FLAT (h4/list/MAP f l)
% Goal: !l. h4/list/LIST__BIND l h4/combin/I = h4/list/FLAT l
%   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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_lists_MAPu_u_IDu_c0]: !_0. (!x. happ _0 x = x) ==> (!l. h4/list/MAP _0 l = l)
% Assm [h4s_lists_MAPu_u_IDu_c1]: !l. h4/list/MAP h4/combin/I l = l
% Assm [h4s_lists_LISTu_u_BINDu_u_DEF]: !l f. h4/list/LIST__BIND l f = h4/list/FLAT (h4/list/MAP f l)
% Goal: !l. h4/list/LIST__BIND l h4/combin/I = h4/list/FLAT l
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_Q247491,TV_Q247487]: ![V_f, V_g]: (![V_x]: s(TV_Q247487,happ(s(t_fun(TV_Q247491,TV_Q247487),V_f),s(TV_Q247491,V_x))) = s(TV_Q247487,happ(s(t_fun(TV_Q247491,TV_Q247487),V_g),s(TV_Q247491,V_x))) => s(t_fun(TV_Q247491,TV_Q247487),V_f) = s(t_fun(TV_Q247491,TV_Q247487),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_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_lists_MAPu_u_IDu_c0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_uu_0),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x) => ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27a),V_uu_0),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l))).
fof(ah4s_lists_MAPu_u_IDu_c1, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_LISTu_u_BINDu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_l, V_f]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_bind(s(t_h4s_lists_list(TV_u_27b),V_l),s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27a)),V_f))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_map(s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27a)),V_f),s(t_h4s_lists_list(TV_u_27b),V_l)))))).
fof(ch4s_lists_LISTu_u_BINDu_u_IDu_c1, conjecture, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_listu_u_bind(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_l),s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_combins_i))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_l)))).
