%   ORIGINAL: h4/finite__map/f__o__FEMPTY
% 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/finite__map/f__o__f__FEMPTY__1: !f. h4/finite__map/f__o__f h4/finite__map/FEMPTY f = h4/finite__map/FEMPTY
% Assm: h4/finite__map/f__o__DEF: !g f. h4/finite__map/f__o f g = h4/finite__map/f__o__f f (h4/finite__map/FUN__FMAP g (h4/pred__set/GSPEC (\x. h4/pair/_2C x (h4/bool/IN (g x) (h4/finite__map/FDOM f)))))
% Goal: !g. h4/finite__map/f__o h4/finite__map/FEMPTY g = h4/finite__map/FEMPTY
%   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_finiteu_u_maps_fu_u_ou_u_fu_u_FEMPTYu_u_1]: !f. h4/finite__map/f__o__f h4/finite__map/FEMPTY f = h4/finite__map/FEMPTY
% Assm [h4s_finiteu_u_maps_fu_u_ou_u_DEF]: !_0. (!g f x. happ (happ (happ _0 g) f) x = h4/pair/_2C x (h4/bool/IN (happ g x) (h4/finite__map/FDOM f))) ==> (!g f. h4/finite__map/f__o f g = h4/finite__map/f__o__f f (h4/finite__map/FUN__FMAP g (h4/pred__set/GSPEC (happ (happ _0 g) f))))
% Goal: !g. h4/finite__map/f__o h4/finite__map/FEMPTY g = h4/finite__map/FEMPTY
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_Q74911,TV_Q74907]: ![V_f, V_g]: (![V_x]: s(TV_Q74907,happ(s(t_fun(TV_Q74911,TV_Q74907),V_f),s(TV_Q74911,V_x))) = s(TV_Q74907,happ(s(t_fun(TV_Q74911,TV_Q74907),V_g),s(TV_Q74911,V_x))) => s(t_fun(TV_Q74911,TV_Q74907),V_f) = s(t_fun(TV_Q74911,TV_Q74907),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_finiteu_u_maps_fu_u_ou_u_fu_u_FEMPTYu_u_1, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_f]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27c),h4s_finiteu_u_maps_fu_u_ou_u_f(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),h4s_finiteu_u_maps_fempty),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_f))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27c),h4s_finiteu_u_maps_fempty)).
fof(ah4s_finiteu_u_maps_fu_u_ou_u_DEF, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_uu_0]: (![V_g, V_f, V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),V_f))),s(TV_u_27a,V_x))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_bool,h4s_bools_in(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_27b,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),V_f))))))) => ![V_g, V_f]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27c),h4s_finiteu_u_maps_fu_u_o(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27c),h4s_finiteu_u_maps_fu_u_ou_u_f(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),V_f),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),h4s_finiteu_u_maps_funu_u_fmap(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),V_f))))))))))).
fof(ch4s_finiteu_u_maps_fu_u_ou_u_FEMPTY, conjecture, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_g]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27c),h4s_finiteu_u_maps_fu_u_o(s(t_h4s_finiteu_u_maps_fmap(TV_u_27b,TV_u_27c),h4s_finiteu_u_maps_fempty),s(t_fun(TV_u_27a,TV_u_27b),V_g))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27c),h4s_finiteu_u_maps_fempty)).
