%   ORIGINAL: h4/quotient__option/OPTION__MAP__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/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/option/option__nchotomy: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm: h4/option/OPTION__MAP__DEF_c0: !x f. h4/option/OPTION__MAP f (h4/option/SOME x) = h4/option/SOME (f x)
% Assm: h4/option/OPTION__MAP__DEF_c1: !f. h4/option/OPTION__MAP f h4/option/NONE = h4/option/NONE
% Assm: h4/quotient/FUN__REL__MP: !rep1 abs1 R1. h4/quotient/QUOTIENT R1 abs1 rep1 ==> (!R2 abs2 rep2. h4/quotient/QUOTIENT R2 abs2 rep2 ==> (!f g x y. h4/quotient/_3D_3D_3D_3E R1 R2 f g /\ R1 x y ==> R2 (f x) (g y)))
% Assm: h4/quotient__option/OPTION__REL__def_c0: !R. h4/option/OPTREL R h4/option/NONE h4/option/NONE <=> T
% Assm: h4/quotient__option/OPTION__REL__def_c1: !x R. h4/option/OPTREL R (h4/option/SOME x) h4/option/NONE <=> F
% Assm: h4/quotient__option/OPTION__REL__def_c2: !y R. h4/option/OPTREL R h4/option/NONE (h4/option/SOME y) <=> F
% 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: !rep1 abs1 R1. h4/quotient/QUOTIENT R1 abs1 rep1 ==> (!R2 abs2 rep2. h4/quotient/QUOTIENT R2 abs2 rep2 ==> (!a1 a2 f1 f2. h4/quotient/_3D_3D_3D_3E R1 R2 f1 f2 /\ h4/option/OPTREL R1 a1 a2 ==> h4/option/OPTREL R2 (h4/option/OPTION__MAP f1 a1) (h4/option/OPTION__MAP f2 a2)))
%   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_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_options_optionu_u_nchotomy]: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm [h4s_options_OPTIONu_u_MAPu_u_DEFu_c0]: !x f. h4/option/OPTION__MAP f (h4/option/SOME x) = h4/option/SOME (happ f x)
% Assm [h4s_options_OPTIONu_u_MAPu_u_DEFu_c1]: !f. h4/option/OPTION__MAP f h4/option/NONE = h4/option/NONE
% Assm [h4s_quotients_FUNu_u_RELu_u_MP]: !rep1 abs1 R1. h4/quotient/QUOTIENT R1 abs1 rep1 ==> (!R2 abs2 rep2. h4/quotient/QUOTIENT R2 abs2 rep2 ==> (!f g x y. h4/quotient/_3D_3D_3D_3E R1 R2 f g /\ happ (happ R1 x) y ==> happ (happ R2 (happ f x)) (happ g y)))
% Assm [h4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c0]: !R. h4/option/OPTREL R h4/option/NONE h4/option/NONE <=> T
% Assm [h4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c1]: !x R. h4/option/OPTREL R (h4/option/SOME x) h4/option/NONE <=> F
% Assm [h4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c2]: !y R. h4/option/OPTREL R h4/option/NONE (h4/option/SOME y) <=> F
% 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: !rep1 abs1 R1. h4/quotient/QUOTIENT R1 abs1 rep1 ==> (!R2 abs2 rep2. h4/quotient/QUOTIENT R2 abs2 rep2 ==> (!a1 a2 f1 f2. h4/quotient/_3D_3D_3D_3E R1 R2 f1 f2 /\ h4/option/OPTREL R1 a1 a2 ==> h4/option/OPTREL R2 (h4/option/OPTION__MAP f1 a1) (h4/option/OPTION__MAP f2 a2)))
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_Q205597,TV_Q205593]: ![V_f, V_g]: (![V_x]: s(TV_Q205593,happ(s(t_fun(TV_Q205597,TV_Q205593),V_f),s(TV_Q205597,V_x))) = s(TV_Q205593,happ(s(t_fun(TV_Q205597,TV_Q205593),V_g),s(TV_Q205597,V_x))) => s(t_fun(TV_Q205597,TV_Q205593),V_f) = s(t_fun(TV_Q205597,TV_Q205593),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_options_optionu_u_nchotomy, axiom, ![TV_u_27a]: ![V_opt]: (s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) | ?[V_x]: s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
fof(ah4s_options_OPTIONu_u_MAPu_u_DEFu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(t_h4s_options_option(TV_u_27b),h4s_options_some(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))))).
fof(ah4s_options_OPTIONu_u_MAPu_u_DEFu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_h4s_options_option(TV_u_27b),h4s_options_none)).
fof(ah4s_quotients_FUNu_u_RELu_u_MP, axiom, ![TV_u_27c,TV_u_27d,TV_u_27b,TV_u_27a]: ![V_rep1, V_abs1, V_R1]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27a,TV_u_27c),V_abs1),s(t_fun(TV_u_27c,TV_u_27a),V_rep1)))) => ![V_R2, V_abs2, V_rep2]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_fun(TV_u_27b,TV_u_27d),V_abs2),s(t_fun(TV_u_27d,TV_u_27b),V_rep2)))) => ![V_f, V_g, V_x, V_y]: ((p(s(t_bool,h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g)))) & 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_R1),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_y)))))))))).
fof(ah4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c0, axiom, ![TV_u_27a]: ![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_none),s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_bool,t)).
fof(ah4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c1, axiom, ![TV_u_27a]: ![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_none))) = s(t_bool,f)).
fof(ah4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c2, axiom, ![TV_u_27a]: ![V_y, 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_none),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_y))))) = s(t_bool,f)).
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_OPTIONu_u_MAPu_u_RSP, conjecture, ![TV_u_27c,TV_u_27d,TV_u_27b,TV_u_27a]: ![V_rep1, V_abs1, V_R1]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27a,TV_u_27c),V_abs1),s(t_fun(TV_u_27c,TV_u_27a),V_rep1)))) => ![V_R2, V_abs2, V_rep2]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_fun(TV_u_27b,TV_u_27d),V_abs2),s(t_fun(TV_u_27d,TV_u_27b),V_rep2)))) => ![V_a1, V_a2, V_f1, V_f2]: ((p(s(t_bool,h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(TV_u_27a,TV_u_27b),V_f2)))) & p(s(t_bool,h4s_options_optrel(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_h4s_options_option(TV_u_27a),V_a1),s(t_h4s_options_option(TV_u_27a),V_a2))))) => p(s(t_bool,h4s_options_optrel(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_map(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_h4s_options_option(TV_u_27a),V_a1))),s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_map(s(t_fun(TV_u_27a,TV_u_27b),V_f2),s(t_h4s_options_option(TV_u_27a),V_a2)))))))))).
