%   ORIGINAL: h4/state__transformer/BIND__ASSOC
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/pair/UNCURRY__VAR: !v f. h4/pair/UNCURRY f v = f (h4/pair/FST v) (h4/pair/SND v)
% Assm: h4/state__transformer/BIND__DEF: !g f. h4/state__transformer/BIND g f = h4/combin/o (h4/pair/UNCURRY f) g
% Goal: !n m k. h4/state__transformer/BIND k (\a. h4/state__transformer/BIND (m a) n) = h4/state__transformer/BIND (h4/state__transformer/BIND k m) n
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_combins_ou_u_DEF]: !g f x. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_pairs_UNCURRYu_u_VAR]: !v f. happ (h4/pair/UNCURRY f) v = happ (happ f (h4/pair/FST v)) (h4/pair/SND v)
% Assm [h4s_stateu_u_transformers_BINDu_u_DEF]: !g f. h4/state__transformer/BIND g f = h4/combin/o (h4/pair/UNCURRY f) g
% Goal: !_0. (!m n a. happ (happ (happ _0 m) n) a = h4/state__transformer/BIND (happ m a) n) ==> (!n m k. h4/state__transformer/BIND k (happ (happ _0 m) n) = h4/state__transformer/BIND (h4/state__transformer/BIND k m) n)
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_Q351601,TV_Q351597]: ![V_f, V_g]: (![V_x]: s(TV_Q351597,happ(s(t_fun(TV_Q351601,TV_Q351597),V_f),s(TV_Q351601,V_x))) = s(TV_Q351597,happ(s(t_fun(TV_Q351601,TV_Q351597),V_g),s(TV_Q351601,V_x))) => s(t_fun(TV_Q351601,TV_Q351597),V_f) = s(t_fun(TV_Q351601,TV_Q351597),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: 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_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_pairs_UNCURRYu_u_VAR, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v)))))).
fof(ah4s_stateu_u_transformers_BINDu_u_DEF, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_g, V_f]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,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_g),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_f))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),h4s_combins_o(s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),h4s_pairs_uncurry(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_f))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_g)))).
fof(ch4s_stateu_u_transformers_BINDu_u_ASSOC, conjecture, ![TV_u_27b,TV_u_27c,TV_u_27d,TV_u_27a]: ![V_uu_0]: (![V_m, V_n, V_a]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))))),V_uu_0),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))),s(TV_u_27b,V_a))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m),s(TV_u_27b,V_a))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))) => ![V_n, V_m, V_k]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,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_k),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))))),V_uu_0),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,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_k),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))))).
