%   ORIGINAL: h4/state__transformer/BIND__LEFT__UNIT
% 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/bool/EQ__EXT: !g f. (!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/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/state__transformer/UNIT__DEF: !x. h4/state__transformer/UNIT x = (\s. h4/pair/_2C x s)
% Assm: h4/state__transformer/BIND__DEF: !g f. h4/state__transformer/BIND g f = h4/combin/o (h4/pair/UNCURRY f) g
% Goal: !x k. h4/state__transformer/BIND (h4/state__transformer/UNIT x) k = k x
%   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_bools_EQu_u_EXT]: !g f. (!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_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_stateu_u_transformers_UNITu_u_DEF]: !x x. happ (h4/state__transformer/UNIT x) x = h4/pair/_2C x x
% 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: !x k. h4/state__transformer/BIND (h4/state__transformer/UNIT x) k = happ k x
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_Q351526,TV_Q351522]: ![V_f, V_g]: (![V_x]: s(TV_Q351522,happ(s(t_fun(TV_Q351526,TV_Q351522),V_f),s(TV_Q351526,V_x))) = s(TV_Q351522,happ(s(t_fun(TV_Q351526,TV_Q351522),V_g),s(TV_Q351526,V_x))) => s(t_fun(TV_Q351526,TV_Q351522),V_f) = s(t_fun(TV_Q351526,TV_Q351522),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_bools_EQu_u_EXT, axiom, ![TV_u_27a,TV_u_27b]: ![V_g, V_f]: (![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_x))) => s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),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_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, 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),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = 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,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_stateu_u_transformers_UNITu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_unit(s(TV_u_27b,V_x))),s(TV_u_27a,V_x0))) = s(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27a,V_x0)))).
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_LEFTu_u_UNIT, conjecture, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_x, V_k]: s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_stateu_u_transformers_unit(s(TV_u_27a,V_x))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_k))) = s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_k),s(TV_u_27a,V_x)))).
