%   ORIGINAL: h4/bool/FALSITY
% 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/F__DEF: F <=> (!t. t)
% Goal: !t. F ==> t
%   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_Fu_u_DEF]: F <=> (!t. t)
% Goal: !t. F ==> t
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q290039,TV_Q290035]: ![V_f, V_g]: (![V_x]: s(TV_Q290035,happ(s(t_fun(TV_Q290039,TV_Q290035),V_f),s(TV_Q290039,V_x))) = s(TV_Q290035,happ(s(t_fun(TV_Q290039,TV_Q290035),V_g),s(TV_Q290039,V_x))) => s(t_fun(TV_Q290039,TV_Q290035),V_f) = s(t_fun(TV_Q290039,TV_Q290035),V_g))).
fof(ah4s_bools_Fu_u_DEF, axiom, (p(s(t_bool,f)) <=> ![V_t]: p(s(t_bool,V_t)))).
fof(ch4s_bools_FALSITY, conjecture, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
