%   ORIGINAL: h4/bool/itself__induction
% 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/ITSELF__UNIQUE: !i. i = h4/bool/the__value
% Goal: !P. P h4/bool/the__value ==> (!i. P 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_ITSELFu_u_UNIQUE]: !i. i = h4/bool/the__value
% Goal: !P. happ P h4/bool/the__value ==> (!i. happ P 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_Q294240,TV_Q294236]: ![V_f, V_g]: (![V_x]: s(TV_Q294236,happ(s(t_fun(TV_Q294240,TV_Q294236),V_f),s(TV_Q294240,V_x))) = s(TV_Q294236,happ(s(t_fun(TV_Q294240,TV_Q294236),V_g),s(TV_Q294240,V_x))) => s(t_fun(TV_Q294240,TV_Q294236),V_f) = s(t_fun(TV_Q294240,TV_Q294236),V_g))).
fof(ah4s_bools_ITSELFu_u_UNIQUE, axiom, ![TV_u_27a]: ![V_i]: s(t_h4s_bools_itself(TV_u_27a),V_i) = s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)).
fof(ch4s_bools_itselfu_u_induction, conjecture, ![TV_u_27a]: ![V_P]: (p(s(t_bool,happ(s(t_fun(t_h4s_bools_itself(TV_u_27a),t_bool),V_P),s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))) => ![V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_bools_itself(TV_u_27a),t_bool),V_P),s(t_h4s_bools_itself(TV_u_27a),V_i)))))).
