%   ORIGINAL: h4/quotient__option/SOME__RSP
% 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/TRUTH: T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/quotient__option/OPTION__REL__def_c3: !y x R. h4/option/OPTREL R (h4/option/SOME x) (h4/option/SOME y) <=> R x y
% Goal: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!x y. R x y ==> h4/option/OPTREL R (h4/option/SOME x) (h4/option/SOME y))
%   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_TRUTH]: T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c3]: !y x R. h4/option/OPTREL R (h4/option/SOME x) (h4/option/SOME y) <=> happ (happ R x) y
% Goal: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!x y. happ (happ R x) y ==> h4/option/OPTREL R (h4/option/SOME x) (h4/option/SOME y))
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_Q205447,TV_Q205443]: ![V_f, V_g]: (![V_x]: s(TV_Q205443,happ(s(t_fun(TV_Q205447,TV_Q205443),V_f),s(TV_Q205447,V_x))) = s(TV_Q205443,happ(s(t_fun(TV_Q205447,TV_Q205443),V_g),s(TV_Q205447,V_x))) => s(t_fun(TV_Q205447,TV_Q205443),V_f) = s(t_fun(TV_Q205447,TV_Q205443),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c3, axiom, ![TV_u_27a]: ![V_y, V_x, V_R]: s(t_bool,h4s_options_optrel(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_y))))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))).
fof(ch4s_quotientu_u_options_SOMEu_u_RSP, conjecture, ![TV_u_27b,TV_u_27a]: ![V_rep, V_abs, V_R]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) => p(s(t_bool,h4s_options_optrel(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_y))))))))).
