%   ORIGINAL: h4/state__transformer/mapM__nil
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/state__transformer/mapM__def: !f. h4/state__transformer/mapM f = h4/combin/o h4/state__transformer/sequence (h4/list/MAP f)
% Assm: h4/state__transformer/sequence__nil: h4/state__transformer/sequence h4/list/NIL = h4/state__transformer/UNIT h4/list/NIL
% Goal: !f. h4/state__transformer/mapM f h4/list/NIL = h4/state__transformer/UNIT h4/list/NIL
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_lists_MAP0u_c0]: !f. happ (h4/list/MAP f) h4/list/NIL = h4/list/NIL
% Assm [h4s_stateu_u_transformers_mapMu_u_def]: !f. h4/state__transformer/mapM f = h4/combin/o h4/state__transformer/sequence (h4/list/MAP f)
% Assm [h4s_stateu_u_transformers_sequenceu_u_nil]: happ h4/state__transformer/sequence h4/list/NIL = h4/state__transformer/UNIT h4/list/NIL
% Goal: !f. happ (h4/state__transformer/mapM f) h4/list/NIL = h4/state__transformer/UNIT h4/list/NIL
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_Q351926,TV_Q351922]: ![V_f, V_g]: (![V_x]: s(TV_Q351922,happ(s(t_fun(TV_Q351926,TV_Q351922),V_f),s(TV_Q351926,V_x))) = s(TV_Q351922,happ(s(t_fun(TV_Q351926,TV_Q351922),V_g),s(TV_Q351926,V_x))) => s(t_fun(TV_Q351926,TV_Q351922),V_f) = s(t_fun(TV_Q351926,TV_Q351922),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![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_f))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_stateu_u_transformers_mapMu_u_def, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_f]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27b))),h4s_stateu_u_transformers_mapm(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_f))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27b))),h4s_combins_o(s(t_fun(t_h4s_lists_list(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),t_fun(TV_u_27b,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27c),TV_u_27b))),h4s_stateu_u_transformers_sequence),s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b)))),h4s_lists_map(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_f)))))).
fof(ah4s_stateu_u_transformers_sequenceu_u_nil, axiom, ![TV_u_27a,TV_u_27b]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),h4s_stateu_u_transformers_sequence),s(t_h4s_lists_list(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),h4s_stateu_u_transformers_unit(s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)))).
fof(ch4s_stateu_u_transformers_mapMu_u_nil, conjecture, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_f]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),h4s_stateu_u_transformers_mapm(s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),V_f))),s(t_h4s_lists_list(TV_u_27c),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),h4s_stateu_u_transformers_unit(s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)))).
