%   ORIGINAL: h4/lbtree/finite__map
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/LEFT__FORALL__OR__THM: !Q P. (!x. P x \/ Q) <=> (!x. P x) \/ Q
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/lbtree/map__def_c0: !f. h4/lbtree/map f h4/lbtree/Lf = h4/lbtree/Lf
% Assm: h4/lbtree/map__def_c1: !t2 t1 f a. h4/lbtree/map f (h4/lbtree/Nd a t1 t2) = h4/lbtree/Nd (f a) (h4/lbtree/map f t1) (h4/lbtree/map f t2)
% Assm: h4/lbtree/map__eq__Lf_c1: !t f. h4/lbtree/Lf = h4/lbtree/map f t <=> t = h4/lbtree/Lf
% Assm: h4/lbtree/map__eq__Nd: !t2 t1 t f a. h4/lbtree/map f t = h4/lbtree/Nd a t1 t2 <=> (?a_27 t1_27 t2_27. t = h4/lbtree/Nd a_27 t1_27 t2_27 /\ a = f a_27 /\ t1 = h4/lbtree/map f t1_27 /\ t2 = h4/lbtree/map f t2_27)
% Assm: h4/lbtree/finite__def: h4/lbtree/finite = (\a0. !finite_27. (!a00. a00 = h4/lbtree/Lf \/ (?a t1 t2. a00 = h4/lbtree/Nd a t1 t2 /\ finite_27 t1 /\ finite_27 t2) ==> finite_27 a00) ==> finite_27 a0)
% Assm: h4/lbtree/finite__thm_c0: h4/lbtree/finite h4/lbtree/Lf <=> T
% Assm: h4/lbtree/finite__thm_c1: !t2 t1 a. h4/lbtree/finite (h4/lbtree/Nd a t1 t2) <=> h4/lbtree/finite t1 /\ h4/lbtree/finite t2
% Goal: !t f. h4/lbtree/finite (h4/lbtree/map f t) <=> h4/lbtree/finite t
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% 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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. happ P x \/ Q) <=> (!x. happ P x) \/ Q
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_lbtrees_mapu_u_defu_c0]: !f. h4/lbtree/map f h4/lbtree/Lf = h4/lbtree/Lf
% Assm [h4s_lbtrees_mapu_u_defu_c1]: !t2 t1 f a. h4/lbtree/map f (h4/lbtree/Nd a t1 t2) = h4/lbtree/Nd (happ f a) (h4/lbtree/map f t1) (h4/lbtree/map f t2)
% Assm [h4s_lbtrees_mapu_u_equ_u_Lfu_c1]: !t f. h4/lbtree/Lf = h4/lbtree/map f t <=> t = h4/lbtree/Lf
% Assm [h4s_lbtrees_mapu_u_equ_u_Nd]: !t2 t1 t f a. h4/lbtree/map f t = h4/lbtree/Nd a t1 t2 <=> (?a_27 t1_27 t2_27. t = h4/lbtree/Nd a_27 t1_27 t2_27 /\ a = happ f a_27 /\ t1 = h4/lbtree/map f t1_27 /\ t2 = h4/lbtree/map f t2_27)
% Assm [h4s_lbtrees_finiteu_u_def]: !x. h4/lbtree/finite x <=> (!finite_27. (!a00. a00 = h4/lbtree/Lf \/ (?a t1 t2. a00 = h4/lbtree/Nd a t1 t2 /\ happ finite_27 t1 /\ happ finite_27 t2) ==> happ finite_27 a00) ==> happ finite_27 x)
% Assm [h4s_lbtrees_finiteu_u_thmu_c0]: h4/lbtree/finite h4/lbtree/Lf <=> T
% Assm [h4s_lbtrees_finiteu_u_thmu_c1]: !t2 t1 a. h4/lbtree/finite (h4/lbtree/Nd a t1 t2) <=> h4/lbtree/finite t1 /\ h4/lbtree/finite t2
% Goal: !t f. h4/lbtree/finite (h4/lbtree/map f t) <=> h4/lbtree/finite t
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q197969,TV_Q197965]: ![V_f, V_g]: (![V_x]: s(TV_Q197965,happ(s(t_fun(TV_Q197969,TV_Q197965),V_f),s(TV_Q197969,V_x))) = s(TV_Q197965,happ(s(t_fun(TV_Q197969,TV_Q197965),V_g),s(TV_Q197969,V_x))) => s(t_fun(TV_Q197969,TV_Q197965),V_f) = s(t_fun(TV_Q197969,TV_Q197965),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,t0))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t0))) <=> p(s(t_bool,t0)))).
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,t0)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
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,t0)))).
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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,V_Q))) <=> (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,V_Q))))).
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_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => p(s(t_bool,f0))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_lbtrees_mapu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_lf))) = s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_lf)).
fof(ah4s_lbtrees_mapu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t2, V_t1, V_f, V_a]: s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_nd(s(TV_u_27a,V_a),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t1),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t2))))) = s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_nd(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_a))),s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t1))),s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t2)))))).
fof(ah4s_lbtrees_mapu_u_equ_u_Lfu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_t, V_f]: (s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_lf) = s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_map(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t))) <=> s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t) = s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_lf))).
fof(ah4s_lbtrees_mapu_u_equ_u_Nd, axiom, ![TV_u_27a,TV_u_27b]: ![V_t2, V_t1, V_t, V_f, V_a]: (s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_map(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t))) = s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_nd(s(TV_u_27a,V_a),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t1),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t2))) <=> ?[V_au_27, V_t1u_27, V_t2u_27]: (s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t) = s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_nd(s(TV_u_27b,V_au_27),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t1u_27),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t2u_27))) & (s(TV_u_27a,V_a) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(TV_u_27b,V_au_27))) & (s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t1) = s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_map(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t1u_27))) & s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t2) = s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_map(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t2u_27)))))))).
fof(ah4s_lbtrees_finiteu_u_def, axiom, ![TV_u_27a]: ![V_x]: (p(s(t_bool,h4s_lbtrees_finite(s(t_h4s_lbtrees_lbtree(TV_u_27a),V_x)))) <=> ![V_finiteu_27]: (![V_a00]: ((s(t_h4s_lbtrees_lbtree(TV_u_27a),V_a00) = s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_lf) | ?[V_a, V_t1, V_t2]: (s(t_h4s_lbtrees_lbtree(TV_u_27a),V_a00) = s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_nd(s(TV_u_27a,V_a),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t1),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t2))) & (p(s(t_bool,happ(s(t_fun(t_h4s_lbtrees_lbtree(TV_u_27a),t_bool),V_finiteu_27),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t1)))) & p(s(t_bool,happ(s(t_fun(t_h4s_lbtrees_lbtree(TV_u_27a),t_bool),V_finiteu_27),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_t2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lbtrees_lbtree(TV_u_27a),t_bool),V_finiteu_27),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lbtrees_lbtree(TV_u_27a),t_bool),V_finiteu_27),s(t_h4s_lbtrees_lbtree(TV_u_27a),V_x))))))).
fof(ah4s_lbtrees_finiteu_u_thmu_c0, axiom, ![TV_u_27a]: s(t_bool,h4s_lbtrees_finite(s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_lf))) = s(t_bool,t0)).
fof(ah4s_lbtrees_finiteu_u_thmu_c1, axiom, ![TV_u_27b]: ![V_t2, V_t1, V_a]: (p(s(t_bool,h4s_lbtrees_finite(s(t_h4s_lbtrees_lbtree(TV_u_27b),h4s_lbtrees_nd(s(TV_u_27b,V_a),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t1),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t2)))))) <=> (p(s(t_bool,h4s_lbtrees_finite(s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t1)))) & p(s(t_bool,h4s_lbtrees_finite(s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t2))))))).
fof(ch4s_lbtrees_finiteu_u_map, conjecture, ![TV_u_27a,TV_u_27b]: ![V_t, V_f]: s(t_bool,h4s_lbtrees_finite(s(t_h4s_lbtrees_lbtree(TV_u_27a),h4s_lbtrees_map(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t))))) = s(t_bool,h4s_lbtrees_finite(s(t_h4s_lbtrees_lbtree(TV_u_27b),V_t)))).
