%   ORIGINAL: h4/state__transformer/UNIT__UNCURRY
% 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/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = 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/UNIT__DEF: !x. h4/state__transformer/UNIT x = (\s. h4/pair/_2C x s)
% Goal: !s. h4/pair/UNCURRY h4/state__transformer/UNIT s = s
%   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_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_UNCURRYu_u_VAR]: !v f. h4/pair/UNCURRY f v = happ (happ f (h4/pair/FST v)) (h4/pair/SND v)
% Assm [h4s_stateu_u_transformers_UNITu_u_DEF]: !x x. happ (happ h4/state__transformer/UNIT x) x = h4/pair/_2C x x
% Goal: !s. h4/pair/UNCURRY h4/state__transformer/UNIT s = s
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_Q351551,TV_Q351547]: ![V_f, V_g]: (![V_x]: s(TV_Q351547,happ(s(t_fun(TV_Q351551,TV_Q351547),V_f),s(TV_Q351551,V_x))) = s(TV_Q351547,happ(s(t_fun(TV_Q351551,TV_Q351547),V_g),s(TV_Q351551,V_x))) => s(t_fun(TV_Q351551,TV_Q351547),V_f) = s(t_fun(TV_Q351551,TV_Q351547),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_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),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,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_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)),happ(s(t_fun(TV_u_27b,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(ch4s_stateu_u_transformers_UNITu_u_UNCURRY, conjecture, ![TV_u_27a,TV_u_27b]: ![V_s]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_stateu_u_transformers_unit),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_s))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_s)).
