%   ORIGINAL: h4/state__transformer/JOIN__MMAP__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/ETA__AX: !t. (\x. t x) = t
% 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__SYM__EQ: !y x. x = y <=> y = x
% 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/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/state__transformer/MMAP__DEF: !m f. h4/state__transformer/MMAP f m = h4/state__transformer/BIND m (h4/combin/o h4/state__transformer/UNIT f)
% Assm: h4/state__transformer/JOIN__DEF: !z. h4/state__transformer/JOIN z = h4/state__transformer/BIND z h4/combin/I
% Assm: h4/state__transformer/BIND__LEFT__UNIT: !x k. h4/state__transformer/BIND (h4/state__transformer/UNIT x) k = k x
% Assm: h4/state__transformer/BIND__RIGHT__UNIT: !k. h4/state__transformer/BIND k h4/state__transformer/UNIT = k
% Assm: h4/state__transformer/BIND__ASSOC: !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
% Goal: h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP h4/state__transformer/UNIT) = h4/combin/I
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% 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_SYMu_u_EQ]: !y x. x = y <=> y = x
% 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_combins_Iu_u_THM]: !x. happ h4/combin/I x = x
% Assm [h4s_stateu_u_transformers_MMAPu_u_DEF]: !m f. happ (h4/state__transformer/MMAP f) m = h4/state__transformer/BIND m (h4/combin/o h4/state__transformer/UNIT f)
% Assm [h4s_stateu_u_transformers_JOINu_u_DEF]: !z. happ h4/state__transformer/JOIN z = h4/state__transformer/BIND z h4/combin/I
% Assm [h4s_stateu_u_transformers_BINDu_u_LEFTu_u_UNIT]: !x k. h4/state__transformer/BIND (happ h4/state__transformer/UNIT x) k = happ k x
% Assm [h4s_stateu_u_transformers_BINDu_u_RIGHTu_u_UNIT]: !k. h4/state__transformer/BIND k h4/state__transformer/UNIT = k
% Assm [h4s_stateu_u_transformers_BINDu_u_ASSOC]: !_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)
% Goal: h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP h4/state__transformer/UNIT) = h4/combin/I
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_Q351751,TV_Q351747]: ![V_f, V_g]: (![V_x]: s(TV_Q351747,happ(s(t_fun(TV_Q351751,TV_Q351747),V_f),s(TV_Q351751,V_x))) = s(TV_Q351747,happ(s(t_fun(TV_Q351751,TV_Q351747),V_g),s(TV_Q351751,V_x))) => s(t_fun(TV_Q351751,TV_Q351747),V_f) = s(t_fun(TV_Q351751,TV_Q351747),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
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_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
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_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_stateu_u_transformers_MMAPu_u_DEF, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_m, V_f]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),V_m))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_bind(s(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_27b,TV_u_27a))),h4s_combins_o(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(t_fun(TV_u_27c,TV_u_27b),V_f)))))).
fof(ah4s_stateu_u_transformers_JOINu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_z]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),V_z))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),V_z),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_i)))).
fof(ah4s_stateu_u_transformers_BINDu_u_LEFTu_u_UNIT, axiom, ![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)),happ(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(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)))).
fof(ah4s_stateu_u_transformers_BINDu_u_RIGHTu_u_UNIT, axiom, ![TV_u_27b,TV_u_27a]: ![V_k]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(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_k),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(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_k)).
fof(ah4s_stateu_u_transformers_BINDu_u_ASSOC, axiom, ![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))))).
fof(ch4s_stateu_u_transformers_JOINu_u_MMAPu_u_UNIT, conjecture, ![TV_u_27b,TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(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_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a))),h4s_stateu_u_transformers_mmap(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(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_i)).
