%   ORIGINAL: h4/list/MAP__MAP__o
% 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/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/list/MAP__o: !g f. h4/list/MAP (h4/combin/o f g) = h4/combin/o (h4/list/MAP f) (h4/list/MAP g)
% Goal: !l g f. h4/list/MAP f (h4/list/MAP g l) = h4/list/MAP (h4/combin/o f g) 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_combins_ou_u_DEF]: !g f x. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_lists_MAPu_u_o]: !g f. h4/list/MAP (h4/combin/o f g) = h4/combin/o (h4/list/MAP f) (h4/list/MAP g)
% Goal: !l g f. happ (h4/list/MAP f) (happ (h4/list/MAP g) l) = happ (h4/list/MAP (h4/combin/o f g)) l
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_Q239928,TV_Q239924]: ![V_f, V_g]: (![V_x]: s(TV_Q239924,happ(s(t_fun(TV_Q239928,TV_Q239924),V_f),s(TV_Q239928,V_x))) = s(TV_Q239924,happ(s(t_fun(TV_Q239928,TV_Q239924),V_g),s(TV_Q239928,V_x))) => s(t_fun(TV_Q239928,TV_Q239924),V_f) = s(t_fun(TV_Q239928,TV_Q239924),V_g))).
fof(ah4s_combins_ou_u_DEF, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x)))))).
fof(ah4s_lists_MAPu_u_o, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_g, V_f]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27c)),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27c)),h4s_combins_o(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_lists_map(s(t_fun(TV_u_27b,TV_u_27c),V_f))),s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_g)))))).
fof(ch4s_lists_MAPu_u_MAPu_u_o, conjecture, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_l, V_g, V_f]: s(t_h4s_lists_list(TV_u_27c),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_lists_map(s(t_fun(TV_u_27b,TV_u_27c),V_f))),s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27c),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27c)),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27c),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
