%   ORIGINAL: h4/option/option__CLAUSES_c7
% 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/option/NOT__IS__SOME__EQ__NONE: !x. ~h4/option/IS__SOME x <=> x = h4/option/NONE
% Goal: !x. ~h4/option/IS__SOME x <=> x = h4/option/NONE
%   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_options_NOTu_u_ISu_u_SOMEu_u_EQu_u_NONE]: !x. ~h4/option/IS__SOME x <=> x = h4/option/NONE
% Goal: !x. ~h4/option/IS__SOME x <=> x = h4/option/NONE
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_Q58649,TV_Q58645]: ![V_f, V_g]: (![V_x]: s(TV_Q58645,happ(s(t_fun(TV_Q58649,TV_Q58645),V_f),s(TV_Q58649,V_x))) = s(TV_Q58645,happ(s(t_fun(TV_Q58649,TV_Q58645),V_g),s(TV_Q58649,V_x))) => s(t_fun(TV_Q58649,TV_Q58645),V_f) = s(t_fun(TV_Q58649,TV_Q58645),V_g))).
fof(ah4s_options_NOTu_u_ISu_u_SOMEu_u_EQu_u_NONE, axiom, ![TV_u_27a]: ![V_x]: (~ (p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(TV_u_27a),V_x))))) <=> s(t_h4s_options_option(TV_u_27a),V_x) = s(t_h4s_options_option(TV_u_27a),h4s_options_none))).
fof(ch4s_options_optionu_u_CLAUSESu_c7, conjecture, ![TV_u_27a]: ![V_x]: (~ (p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(TV_u_27a),V_x))))) <=> s(t_h4s_options_option(TV_u_27a),V_x) = s(t_h4s_options_option(TV_u_27a),h4s_options_none))).
