%   ORIGINAL: h4/option/option__CLAUSES_c1
% 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/THE__DEF: !x. h4/option/THE (h4/option/SOME x) = x
% Goal: !x. h4/option/THE (h4/option/SOME x) = x
%   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_THEu_u_DEF]: !x. h4/option/THE (h4/option/SOME x) = x
% Goal: !x. h4/option/THE (h4/option/SOME x) = x
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_Q58499,TV_Q58495]: ![V_f, V_g]: (![V_x]: s(TV_Q58495,happ(s(t_fun(TV_Q58499,TV_Q58495),V_f),s(TV_Q58499,V_x))) = s(TV_Q58495,happ(s(t_fun(TV_Q58499,TV_Q58495),V_g),s(TV_Q58499,V_x))) => s(t_fun(TV_Q58499,TV_Q58495),V_f) = s(t_fun(TV_Q58499,TV_Q58495),V_g))).
fof(ah4s_options_THEu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_options_the(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x)).
fof(ch4s_options_optionu_u_CLAUSESu_c1, conjecture, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_options_the(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x)).
