%   ORIGINAL: h4/tc/TC__ITER__THM
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/pred__set/IN__UNION: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm: h4/pred__set/UNION__COMM: !t s. h4/pred__set/UNION s t = h4/pred__set/UNION t s
% Assm: h4/pred__set/UNION__EMPTY_c1: !s. h4/pred__set/UNION s h4/pred__set/EMPTY = s
% Assm: h4/pred__set/INSERT__UNION__EQ: !x t s. h4/pred__set/UNION (h4/pred__set/INSERT x s) t = h4/pred__set/INSERT x (h4/pred__set/UNION s t)
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/MEM_c1: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm: h4/list/LIST__TO__SET__THM_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/list/LIST__TO__SET__THM_c1: !t h. h4/list/LIST__TO__SET (h4/list/CONS h t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm: h4/finite__map/FDOM__o__f: !g f. h4/finite__map/FDOM (h4/finite__map/o__f f g) = h4/finite__map/FDOM g
% Assm: h4/tc/subTC__RDOM: !R. h4/tc/subTC R (h4/relation/RDOM R) = h4/relation/TC R
% Assm: h4/tc/subTC__FDOM__RDOM: !f R. h4/tc/subTC R (h4/finite__map/FDOM f) = h4/tc/FMAP__TO__RELN f ==> h4/tc/subTC R (h4/relation/RDOM R) = h4/tc/FMAP__TO__RELN f
% Assm: h4/tc/TC__MOD__LEM: !x s f R. h4/bool/IN x (h4/finite__map/FDOM f) /\ h4/tc/subTC R s = h4/tc/FMAP__TO__RELN f ==> h4/tc/subTC R (h4/pred__set/INSERT x s) = h4/tc/FMAP__TO__RELN (h4/finite__map/o__f (h4/tc/TC__MOD x (h4/finite__map/FAPPLY f x)) f)
% Assm: h4/tc/TC__ITER0_c0: !r. h4/tc/TC__ITER h4/list/NIL r = r
% Assm: h4/tc/TC__ITER0_c1: !x r d. h4/tc/TC__ITER (h4/list/CONS x d) r = h4/tc/TC__ITER d (h4/finite__map/o__f (h4/tc/TC__MOD x (h4/finite__map/FAPPLY r x)) r)
% Goal: !s f d R. h4/pred__set/UNION s (h4/list/LIST__TO__SET d) = h4/finite__map/FDOM f /\ h4/tc/subTC R s = h4/tc/FMAP__TO__RELN f ==> h4/relation/TC R = h4/tc/FMAP__TO__RELN (h4/tc/TC__ITER d f)
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_predu_u_sets_INu_u_UNION]: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm [h4s_predu_u_sets_UNIONu_u_COMM]: !t s. h4/pred__set/UNION s t = h4/pred__set/UNION t s
% Assm [h4s_predu_u_sets_UNIONu_u_EMPTYu_c1]: !s. h4/pred__set/UNION s h4/pred__set/EMPTY = s
% Assm [h4s_predu_u_sets_INSERTu_u_UNIONu_u_EQ]: !x t s. h4/pred__set/UNION (h4/pred__set/INSERT x s) t = h4/pred__set/INSERT x (h4/pred__set/UNION s t)
% Assm [h4s_lists_listu_u_induction]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_lists_MEMu_c1]: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm [h4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c1]: !t h. h4/list/LIST__TO__SET (h4/list/CONS h t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm [h4s_finiteu_u_maps_FDOMu_u_ou_u_f]: !g f. h4/finite__map/FDOM (h4/finite__map/o__f f g) = h4/finite__map/FDOM g
% Assm [h4s_tcs_subTCu_u_RDOM]: !R. h4/tc/subTC R (h4/relation/RDOM R) = h4/relation/TC R
% Assm [h4s_tcs_subTCu_u_FDOMu_u_RDOM]: !f R. h4/tc/subTC R (h4/finite__map/FDOM f) = h4/tc/FMAP__TO__RELN f ==> h4/tc/subTC R (h4/relation/RDOM R) = h4/tc/FMAP__TO__RELN f
% Assm [h4s_tcs_TCu_u_MODu_u_LEM]: !x s f R. h4/bool/IN x (h4/finite__map/FDOM f) /\ h4/tc/subTC R s = h4/tc/FMAP__TO__RELN f ==> h4/tc/subTC R (h4/pred__set/INSERT x s) = h4/tc/FMAP__TO__RELN (h4/finite__map/o__f (h4/tc/TC__MOD x (h4/finite__map/FAPPLY f x)) f)
% Assm [h4s_tcs_TCu_u_ITER0u_c0]: !r. h4/tc/TC__ITER h4/list/NIL r = r
% Assm [h4s_tcs_TCu_u_ITER0u_c1]: !x r d. h4/tc/TC__ITER (h4/list/CONS x d) r = h4/tc/TC__ITER d (h4/finite__map/o__f (h4/tc/TC__MOD x (h4/finite__map/FAPPLY r x)) r)
% Goal: !s f d R. h4/pred__set/UNION s (h4/list/LIST__TO__SET d) = h4/finite__map/FDOM f /\ h4/tc/subTC R s = h4/tc/FMAP__TO__RELN f ==> h4/relation/TC R = h4/tc/FMAP__TO__RELN (h4/tc/TC__ITER d f)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q189948,TV_Q189944]: ![V_f, V_g]: (![V_x]: s(TV_Q189944,happ(s(t_fun(TV_Q189948,TV_Q189944),V_f),s(TV_Q189948,V_x))) = s(TV_Q189944,happ(s(t_fun(TV_Q189948,TV_Q189944),V_g),s(TV_Q189948,V_x))) => s(t_fun(TV_Q189948,TV_Q189944),V_f) = s(t_fun(TV_Q189948,TV_Q189944),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_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_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_predu_u_sets_INu_u_UNION, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_UNIONu_u_COMM, axiom, ![TV_u_27a]: ![V_t, V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_s)))).
fof(ah4s_predu_u_sets_UNIONu_u_EMPTYu_c1, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_fun(TV_u_27a,t_bool),V_s)).
fof(ah4s_predu_u_sets_INSERTu_u_UNIONu_u_EQ, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))),s(t_fun(TV_u_27a,t_bool),V_t))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))).
fof(ah4s_lists_listu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_MEMu_c1, axiom, ![TV_u_27a]: ![V_x, V_t, V_h]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_h) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_t))))))))).
fof(ah4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_lists_LISTu_u_TOu_u_SETu_u_THMu_c1, axiom, ![TV_u_27b]: ![V_t, V_h]: s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,V_h),s(t_h4s_lists_list(TV_u_27b),V_t))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_insert(s(TV_u_27b,V_h),s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),V_t)))))).
fof(ah4s_finiteu_u_maps_FDOMu_u_ou_u_f, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_g, V_f]: s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27c),h4s_finiteu_u_maps_ou_u_f(s(t_fun(TV_u_27b,TV_u_27c),V_f),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_g))))) = s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,TV_u_27b),V_g)))).
fof(ah4s_tcs_subTCu_u_RDOM, axiom, ![TV_u_27a]: ![V_R]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_subtc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),h4s_relations_rdom(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))).
fof(ah4s_tcs_subTCu_u_FDOMu_u_RDOM, axiom, ![TV_u_27a]: ![V_f, V_R]: (s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_subtc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_fmapu_u_tou_u_reln(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f))) => s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_subtc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),h4s_relations_rdom(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_fmapu_u_tou_u_reln(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f))))).
fof(ah4s_tcs_TCu_u_MODu_u_LEM, axiom, ![TV_u_27a]: ![V_x, V_s, V_f, V_R]: ((p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f)))))) & s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_subtc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_fmapu_u_tou_u_reln(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f)))) => s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_subtc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_fmapu_u_tou_u_reln(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_finiteu_u_maps_ou_u_f(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),h4s_tcs_tcu_u_mod(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f),s(TV_u_27a,V_x))))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f))))))).
fof(ah4s_tcs_TCu_u_ITER0u_c0, axiom, ![TV_u_27a]: ![V_r]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_tcu_u_iter(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r)).
fof(ah4s_tcs_TCu_u_ITER0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_d]: s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_tcu_u_iter(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_d))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r))) = s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_tcu_u_iter(s(t_h4s_lists_list(TV_u_27a),V_d),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_finiteu_u_maps_ou_u_f(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),h4s_tcs_tcu_u_mod(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r),s(TV_u_27a,V_x))))),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r)))))).
fof(ch4s_tcs_TCu_u_ITERu_u_THM, conjecture, ![TV_u_27a]: ![V_s, V_f, V_d, V_R]: ((s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_d))))) = s(t_fun(TV_u_27a,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f))) & s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_subtc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_fmapu_u_tou_u_reln(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f)))) => s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_fmapu_u_tou_u_reln(s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_tcu_u_iter(s(t_h4s_lists_list(TV_u_27a),V_d),s(t_h4s_finiteu_u_maps_fmap(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_f))))))).
