%   ORIGINAL: h4/normalForms/EXT__POINT0
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/normalForms/EXT__POINT__DEF: !g f. f (h4/normalForms/EXT__POINT f g) = g (h4/normalForms/EXT__POINT f g) ==> f = g
% Goal: !g f. f (h4/normalForms/EXT__POINT f g) = g (h4/normalForms/EXT__POINT f g) <=> f = g
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_normalFormss_EXTu_u_POINTu_u_DEF]: !g f. happ f (h4/normalForms/EXT__POINT f g) = happ g (h4/normalForms/EXT__POINT f g) ==> f = g
% Goal: !g f. happ f (h4/normalForms/EXT__POINT f g) = happ g (h4/normalForms/EXT__POINT f g) <=> f = g
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_Q78817,TV_Q78813]: ![V_f, V_g]: (![V_x]: s(TV_Q78813,happ(s(t_fun(TV_Q78817,TV_Q78813),V_f),s(TV_Q78817,V_x))) = s(TV_Q78813,happ(s(t_fun(TV_Q78817,TV_Q78813),V_g),s(TV_Q78817,V_x))) => s(t_fun(TV_Q78817,TV_Q78813),V_f) = s(t_fun(TV_Q78817,TV_Q78813),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_normalFormss_EXTu_u_POINTu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_g, V_f]: (s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_normalformss_extu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,h4s_normalformss_extu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))))) => s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g))).
fof(ch4s_normalFormss_EXTu_u_POINT0, conjecture, ![TV_u_27a,TV_u_27b]: ![V_g, V_f]: (s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_normalformss_extu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,h4s_normalformss_extu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))))) <=> s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g))).
