%   ORIGINAL: h4/pair/UNCURRY__VAR
% 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
% Goal: !v f. h4/pair/UNCURRY f v = f (h4/pair/FST v) (h4/pair/SND v)
%   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
% Goal: !v f. h4/pair/UNCURRY f v = happ (happ f (h4/pair/FST v)) (h4/pair/SND v)
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_Q283998,TV_Q283994]: ![V_f, V_g]: (![V_x]: s(TV_Q283994,happ(s(t_fun(TV_Q283998,TV_Q283994),V_f),s(TV_Q283998,V_x))) = s(TV_Q283994,happ(s(t_fun(TV_Q283998,TV_Q283994),V_g),s(TV_Q283998,V_x))) => s(t_fun(TV_Q283998,TV_Q283994),V_f) = s(t_fun(TV_Q283998,TV_Q283994),V_g))).
fof(ch4s_pairs_UNCURRYu_u_VAR, conjecture, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v)))))).
