%   ORIGINAL: h4/list/LENGTH__o__REVERSE_c1
% 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/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/list/LENGTH__REVERSE: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Goal: !f. h4/combin/o h4/list/LENGTH (h4/combin/o h4/list/REVERSE f) = h4/combin/o h4/list/LENGTH f
%   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_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_lists_LENGTHu_u_REVERSE]: !l. happ h4/list/LENGTH (happ h4/list/REVERSE l) = happ h4/list/LENGTH l
% Goal: !f. h4/combin/o h4/list/LENGTH (h4/combin/o h4/list/REVERSE f) = h4/combin/o h4/list/LENGTH f
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_Q248903,TV_Q248899]: ![V_f, V_g]: (![V_x]: s(TV_Q248899,happ(s(t_fun(TV_Q248903,TV_Q248899),V_f),s(TV_Q248903,V_x))) = s(TV_Q248899,happ(s(t_fun(TV_Q248903,TV_Q248899),V_g),s(TV_Q248903,V_x))) => s(t_fun(TV_Q248903,TV_Q248899),V_f) = s(t_fun(TV_Q248903,TV_Q248899),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_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![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))))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_lists_LENGTHu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_nums_num),h4s_lists_length),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_nums_num),h4s_lists_length),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ch4s_lists_LENGTHu_u_ou_u_REVERSEu_c1, conjecture, ![TV_u_27b,TV_u_27c]: ![V_f]: s(t_fun(TV_u_27b,t_h4s_nums_num),h4s_combins_o(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_nums_num),h4s_lists_length),s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27c)),h4s_combins_o(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27c)),h4s_lists_reverse),s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27c)),V_f))))) = s(t_fun(TV_u_27b,t_h4s_nums_num),h4s_combins_o(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_nums_num),h4s_lists_length),s(t_fun(TV_u_27b,t_h4s_lists_list(TV_u_27c)),V_f)))).
