%   ORIGINAL: h4/state__transformer/sequence__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/list/FOLDR0_c0: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm: h4/state__transformer/sequence__def: h4/state__transformer/sequence = h4/list/FOLDR (\m ms. h4/state__transformer/BIND m (\x. h4/state__transformer/BIND ms (\xs. h4/state__transformer/UNIT (h4/list/CONS x xs)))) (h4/state__transformer/UNIT h4/list/NIL)
% Goal: h4/state__transformer/sequence 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_lists_FOLDR0u_c0]: !f e. happ (h4/list/FOLDR f e) h4/list/NIL = e
% Assm [h4s_stateu_u_transformers_sequenceu_u_def]: !_3. (!x xs. happ (happ _3 x) xs = h4/state__transformer/UNIT (h4/list/CONS x xs)) ==> (!_2. (!ms x. happ (happ _2 ms) x = h4/state__transformer/BIND ms (happ _3 x)) ==> (!_1. (!m ms. happ (happ _1 m) ms = h4/state__transformer/BIND m (happ _2 ms)) ==> (!_0. (!m. happ _0 m = happ _1 m) ==> h4/state__transformer/sequence = h4/list/FOLDR _0 (h4/state__transformer/UNIT h4/list/NIL))))
% Goal: happ h4/state__transformer/sequence 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,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_Q351901,TV_Q351897]: ![V_f, V_g]: (![V_x]: s(TV_Q351897,happ(s(t_fun(TV_Q351901,TV_Q351897),V_f),s(TV_Q351901,V_x))) = s(TV_Q351897,happ(s(t_fun(TV_Q351901,TV_Q351897),V_g),s(TV_Q351901,V_x))) => s(t_fun(TV_Q351901,TV_Q351897),V_f) = s(t_fun(TV_Q351901,TV_Q351897),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_lists_FOLDR0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e)).
fof(ah4s_stateu_u_transformers_sequenceu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_3]: (![V_x, V_xs]: 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_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_3),s(TV_u_27b,V_x))),s(t_h4s_lists_list(TV_u_27b),V_xs))) = 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_cons(s(TV_u_27b,V_x),s(t_h4s_lists_list(TV_u_27b),V_xs))))) => ![V_uu_2]: (![V_ms, V_x]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_2),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms))),s(TV_u_27b,V_x))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms),s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_3),s(TV_u_27b,V_x))))) => ![V_uu_1]: (![V_m, V_ms]: 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_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(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))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(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)))),V_uu_1),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_2),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms))))) => ![V_uu_0]: (![V_m]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(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))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(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)))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(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))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(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)))),V_uu_1),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m))) => 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_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_lists_foldr(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(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)))),V_uu_0),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_sequenceu_u_nil, conjecture, ![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)))).
