%   ORIGINAL: h4/pred__set/FINITE__SING
% 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/pred__set/SING__DELETE: !x. h4/pred__set/DELETE (h4/pred__set/INSERT x h4/pred__set/EMPTY) x = h4/pred__set/EMPTY
% Assm: h4/pred__set/FINITE__EMPTY: h4/pred__set/FINITE h4/pred__set/EMPTY
% Assm: h4/pred__set/FINITE__INSERT: !x s. h4/pred__set/FINITE (h4/pred__set/INSERT x s) <=> h4/pred__set/FINITE s
% Goal: !x. h4/pred__set/FINITE (h4/pred__set/INSERT x h4/pred__set/EMPTY)
%   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_predu_u_sets_SINGu_u_DELETE]: !x. h4/pred__set/DELETE (h4/pred__set/INSERT x h4/pred__set/EMPTY) x = h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_FINITEu_u_EMPTY]: h4/pred__set/FINITE h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_FINITEu_u_INSERT]: !x s. h4/pred__set/FINITE (h4/pred__set/INSERT x s) <=> h4/pred__set/FINITE s
% Goal: !x. h4/pred__set/FINITE (h4/pred__set/INSERT x h4/pred__set/EMPTY)
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_Q151305,TV_Q151301]: ![V_f, V_g]: (![V_x]: s(TV_Q151301,happ(s(t_fun(TV_Q151305,TV_Q151301),V_f),s(TV_Q151305,V_x))) = s(TV_Q151301,happ(s(t_fun(TV_Q151305,TV_Q151301),V_g),s(TV_Q151305,V_x))) => s(t_fun(TV_Q151305,TV_Q151301),V_f) = s(t_fun(TV_Q151305,TV_Q151301),V_g))).
fof(ah4s_predu_u_sets_SINGu_u_DELETE, axiom, ![TV_u_27a]: ![V_x]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_predu_u_sets_FINITEu_u_EMPTY, axiom, ![TV_u_27a]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))))).
fof(ah4s_predu_u_sets_FINITEu_u_INSERT, axiom, ![TV_u_27a]: ![V_x, V_s]: s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))) = s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))).
fof(ch4s_predu_u_sets_FINITEu_u_SING, conjecture, ![TV_u_27a]: ![V_x]: p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))))))).
