%   ORIGINAL: h4/path/fromPath__onto
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/path/path__absrep__bijections_c0: !a. h4/path/toPath (h4/path/fromPath a) = a
% Assm: h4/path/path__absrep__bijections_c1: !r. (\x. T) r <=> h4/path/fromPath (h4/path/toPath r) = r
% Goal: !r. ?a. r = h4/path/fromPath a
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_paths_pathu_u_absrepu_u_bijectionsu_c0]: !a. h4/path/toPath (h4/path/fromPath a) = a
% Assm [h4s_paths_pathu_u_absrepu_u_bijectionsu_c1]: !r. T <=> h4/path/fromPath (h4/path/toPath r) = r
% Goal: !r. ?a. r = h4/path/fromPath a
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_Q140476,TV_Q140472]: ![V_f, V_g]: (![V_x]: s(TV_Q140472,happ(s(t_fun(TV_Q140476,TV_Q140472),V_f),s(TV_Q140476,V_x))) = s(TV_Q140472,happ(s(t_fun(TV_Q140476,TV_Q140472),V_g),s(TV_Q140476,V_x))) => s(t_fun(TV_Q140476,TV_Q140472),V_f) = s(t_fun(TV_Q140476,TV_Q140472),V_g))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_paths_pathu_u_absrepu_u_bijectionsu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_a]: s(t_h4s_paths_path(TV_u_27a,TV_u_27b),h4s_paths_topath(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_paths_frompath(s(t_h4s_paths_path(TV_u_27a,TV_u_27b),V_a))))) = s(t_h4s_paths_path(TV_u_27a,TV_u_27b),V_a)).
fof(ah4s_paths_pathu_u_absrepu_u_bijectionsu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_r]: (p(s(t_bool,t)) <=> s(t_h4s_pairs_prod(TV_u_27a,t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_paths_frompath(s(t_h4s_paths_path(TV_u_27a,TV_u_27b),h4s_paths_topath(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),V_r))))) = s(t_h4s_pairs_prod(TV_u_27a,t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),V_r))).
fof(ch4s_paths_fromPathu_u_onto, conjecture, ![TV_u_27a,TV_u_27b]: ![V_r]: ?[V_a]: s(t_h4s_pairs_prod(TV_u_27a,t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),V_r) = s(t_h4s_pairs_prod(TV_u_27a,t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_paths_frompath(s(t_h4s_paths_path(TV_u_27a,TV_u_27b),V_a)))).
