%   ORIGINAL: h4/rich__list/FOLDL__REVERSE
% 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/list/REVERSE__REVERSE: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm: h4/rich__list/FOLDL__FOLDR__REVERSE: !l f e. h4/list/FOLDL f e l = h4/list/FOLDR (\x y. f y x) e (h4/list/REVERSE l)
% Goal: !l f e. h4/list/FOLDL f e (h4/list/REVERSE l) = h4/list/FOLDR (\x y. f y x) e l
%   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_lists_REVERSEu_u_REVERSE]: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm [h4s_richu_u_lists_FOLDLu_u_FOLDRu_u_REVERSE]: !_1. (!f x y. happ (happ (happ _1 f) x) y = happ (happ f y) x) ==> (!_0. (!f x. happ (happ _0 f) x = happ (happ _1 f) x) ==> (!l f e. h4/list/FOLDL f e l = h4/list/FOLDR (happ _0 f) e (h4/list/REVERSE l)))
% Goal: !_1. (!f x y. happ (happ (happ _1 f) x) y = happ (happ f y) x) ==> (!_0. (!f x. happ (happ _0 f) x = happ (happ _1 f) x) ==> (!l f e. h4/list/FOLDL f e (h4/list/REVERSE l) = h4/list/FOLDR (happ _0 f) e l))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q159658,TV_Q159654]: ![V_f, V_g]: (![V_x]: s(TV_Q159654,happ(s(t_fun(TV_Q159658,TV_Q159654),V_f),s(TV_Q159658,V_x))) = s(TV_Q159654,happ(s(t_fun(TV_Q159658,TV_Q159654),V_g),s(TV_Q159658,V_x))) => s(t_fun(TV_Q159658,TV_Q159654),V_f) = s(t_fun(TV_Q159658,TV_Q159654),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_lists_REVERSEu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_richu_u_lists_FOLDLu_u_FOLDRu_u_REVERSE, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_f, V_x, V_y]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))),s(TV_u_27a,V_y))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_f, V_x]: s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) = s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) => ![V_l, V_f, V_e]: s(TV_u_27a,h4s_lists_foldl(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),V_l))) = s(TV_u_27a,h4s_lists_foldr(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27b),V_l)))))))).
fof(ch4s_richu_u_lists_FOLDLu_u_REVERSE, conjecture, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_f, V_x, V_y]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))),s(TV_u_27a,V_y))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_f, V_x]: s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) = s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) => ![V_l, V_f, V_e]: s(TV_u_27a,h4s_lists_foldl(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27b),V_l))))) = s(TV_u_27a,h4s_lists_foldr(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),V_l)))))).
