%   ORIGINAL: h4/fmaptree/fmtree__Axiom
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/fmaptree/fmtreerec__thm: !i h fm. h4/fmaptree/fmtreerec h (h4/fmaptree/FTNode i fm) = h i (h4/finite__map/o__f (h4/fmaptree/fmtreerec h) fm) fm
% Goal: !h. ?f. !i fm. f (h4/fmaptree/FTNode i fm) = h i fm (h4/finite__map/o__f f fm)
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_fmaptrees_fmtreerecu_u_thm]: !i h fm. happ (h4/fmaptree/fmtreerec h) (h4/fmaptree/FTNode i fm) = happ (happ (happ h i) (h4/finite__map/o__f (h4/fmaptree/fmtreerec h) fm)) fm
% Goal: !h. ?f. !i fm. happ f (h4/fmaptree/FTNode i fm) = happ (happ (happ h i) fm) (h4/finite__map/o__f f fm)
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_Q255507,TV_Q255503]: ![V_f, V_g]: (![V_x]: s(TV_Q255503,happ(s(t_fun(TV_Q255507,TV_Q255503),V_f),s(TV_Q255507,V_x))) = s(TV_Q255503,happ(s(t_fun(TV_Q255507,TV_Q255503),V_g),s(TV_Q255507,V_x))) => s(t_fun(TV_Q255507,TV_Q255503),V_f) = s(t_fun(TV_Q255507,TV_Q255503),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_fmaptrees_fmtreerecu_u_thm, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_i, V_h, V_fm]: s(TV_u_27a,happ(s(t_fun(t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b),TV_u_27a),h4s_fmaptrees_fmtreerec(s(t_fun(TV_u_27b,t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,TV_u_27a),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),TV_u_27a))),V_h))),s(t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b),h4s_fmaptrees_ftnode(s(TV_u_27b,V_i),s(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),V_fm))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),TV_u_27a),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,TV_u_27a),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,TV_u_27a),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),TV_u_27a))),V_h),s(TV_u_27b,V_i))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27c,TV_u_27a),h4s_finiteu_u_maps_ou_u_f(s(t_fun(t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b),TV_u_27a),h4s_fmaptrees_fmtreerec(s(t_fun(TV_u_27b,t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,TV_u_27a),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),TV_u_27a))),V_h))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),V_fm))))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27c,t_h4s_fmaptrees_fmaptree(TV_u_27c,TV_u_27b)),V_fm)))).
fof(ch4s_fmaptrees_fmtreeu_u_Axiom, conjecture, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_h]: ?[V_f]: ![V_i, V_fm]: s(TV_u_27c,happ(s(t_fun(t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a),TV_u_27c),V_f),s(t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a),h4s_fmaptrees_ftnode(s(TV_u_27a,V_i),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a)),V_fm))))) = s(TV_u_27c,happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),TV_u_27c),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a)),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),TV_u_27c)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a)),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),TV_u_27c))),V_h),s(TV_u_27a,V_i))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a)),V_fm))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),h4s_finiteu_u_maps_ou_u_f(s(t_fun(t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a),TV_u_27c),V_f),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,t_h4s_fmaptrees_fmaptree(TV_u_27b,TV_u_27a)),V_fm)))))).
