%   ORIGINAL: h4/fmaptree/item__thm
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/fmaptree/FTNode__11: !i2 i1 f2 f1. h4/fmaptree/FTNode i1 f1 = h4/fmaptree/FTNode i2 f2 <=> i1 = i2 /\ f1 = f2
% Assm: h4/fmaptree/item__map__def: !ft. ft = h4/fmaptree/FTNode (h4/fmaptree/item ft) (h4/fmaptree/map ft)
% Goal: !i fm. h4/fmaptree/item (h4/fmaptree/FTNode i fm) = i
%   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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_fmaptrees_FTNodeu_u_11]: !i2 i1 f2 f1. h4/fmaptree/FTNode i1 f1 = h4/fmaptree/FTNode i2 f2 <=> i1 = i2 /\ f1 = f2
% Assm [h4s_fmaptrees_itemu_u_mapu_u_def]: !ft. ft = h4/fmaptree/FTNode (h4/fmaptree/item ft) (h4/fmaptree/map ft)
% Goal: !i fm. h4/fmaptree/item (h4/fmaptree/FTNode i fm) = i
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_Q255256,TV_Q255252]: ![V_f, V_g]: (![V_x]: s(TV_Q255252,happ(s(t_fun(TV_Q255256,TV_Q255252),V_f),s(TV_Q255256,V_x))) = s(TV_Q255252,happ(s(t_fun(TV_Q255256,TV_Q255252),V_g),s(TV_Q255256,V_x))) => s(t_fun(TV_Q255256,TV_Q255252),V_f) = s(t_fun(TV_Q255256,TV_Q255252),V_g))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_fmaptrees_FTNodeu_u_11, axiom, ![TV_u_27a,TV_u_27b]: ![V_i2, V_i1, V_f2, V_f1]: (s(t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b),h4s_fmaptrees_ftnode(s(TV_u_27b,V_i1),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b)),V_f1))) = s(t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b),h4s_fmaptrees_ftnode(s(TV_u_27b,V_i2),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b)),V_f2))) <=> (s(TV_u_27b,V_i1) = s(TV_u_27b,V_i2) & s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b)),V_f1) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b)),V_f2)))).
fof(ah4s_fmaptrees_itemu_u_mapu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_ft]: s(t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b),V_ft) = s(t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b),h4s_fmaptrees_ftnode(s(TV_u_27b,h4s_fmaptrees_item(s(t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b),V_ft))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b)),h4s_fmaptrees_map(s(t_h4s_fmaptrees_fmaptree(TV_u_27a,TV_u_27b),V_ft)))))).
fof(ch4s_fmaptrees_itemu_u_thm, conjecture, ![TV_u_27b,TV_u_27a]: ![V_i, V_fm]: s(TV_u_27a,h4s_fmaptrees_item(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_27a,V_i)).
