%   ORIGINAL: h4/ind__type/CONSTR__INJ
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !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/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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__ALL: !Q P. (!x. P x ==> Q x) ==> (!x. P x) ==> (!x. Q x)
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/prim__rec/INV__SUC__EQ: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm: h4/ind__type/INJN__INJ: !n2 n1. h4/ind__type/INJN n1 = h4/ind__type/INJN n2 <=> n1 = n2
% Assm: h4/ind__type/INJA__INJ: !a2 a1. h4/ind__type/INJA a1 = h4/ind__type/INJA a2 <=> a1 = a2
% Assm: h4/ind__type/INJF__INJ: !f2 f1. h4/ind__type/INJF f1 = h4/ind__type/INJF f2 <=> f1 = f2
% Assm: h4/ind__type/INJP__INJ: !f2_27 f2 f1_27 f1. h4/ind__type/INJP f1 f2 = h4/ind__type/INJP f1_27 f2_27 <=> f1 = f1_27 /\ f2 = f2_27
% Assm: h4/ind__type/ZCONSTR0: !r i c. h4/ind__type/ZCONSTR c i r = h4/ind__type/INJP (h4/ind__type/INJN (h4/num/SUC c)) (h4/ind__type/INJP (h4/ind__type/INJA i) (h4/ind__type/INJF r))
% Assm: h4/ind__type/ZRECSPACE__def: h4/ind__type/ZRECSPACE = (\a0. !ZRECSPACE_27. (!a00. a00 = h4/ind__type/ZBOT \/ (?c i r. a00 = h4/ind__type/ZCONSTR c i r /\ (!n. ZRECSPACE_27 (r n))) ==> ZRECSPACE_27 a00) ==> ZRECSPACE_27 a0)
% Assm: h4/ind__type/recspace__repfns_c0: !a. h4/ind__type/mk__rec (h4/ind__type/dest__rec a) = a
% Assm: h4/ind__type/recspace__repfns_c1: !r. h4/ind__type/ZRECSPACE r <=> h4/ind__type/dest__rec (h4/ind__type/mk__rec r) = r
% Assm: h4/ind__type/CONSTR0: !r i c. h4/ind__type/CONSTR c i r = h4/ind__type/mk__rec (h4/ind__type/ZCONSTR c i (\n. h4/ind__type/dest__rec (r n)))
% Assm: h4/ind__type/MK__REC__INJ: !y x. h4/ind__type/mk__rec x = h4/ind__type/mk__rec y ==> h4/ind__type/ZRECSPACE x /\ h4/ind__type/ZRECSPACE y ==> x = y
% Assm: h4/ind__type/DEST__REC__INJ: !y x. h4/ind__type/dest__rec x = h4/ind__type/dest__rec y <=> x = y
% Goal: !r2 r1 i2 i1 c2 c1. h4/ind__type/CONSTR c1 i1 r1 = h4/ind__type/CONSTR c2 i2 r2 <=> c1 = c2 /\ i1 = i2 /\ r1 = r2
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !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_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% 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_ALL]: !Q P. (!x. happ P x ==> happ Q x) ==> (!x. happ P x) ==> (!x. happ Q x)
% 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_primu_u_recs_INVu_u_SUCu_u_EQ]: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm [h4s_indu_u_types_INJNu_u_INJ]: !n2 n1. h4/ind__type/INJN n1 = h4/ind__type/INJN n2 <=> n1 = n2
% Assm [h4s_indu_u_types_INJAu_u_INJ]: !a2 a1. h4/ind__type/INJA a1 = h4/ind__type/INJA a2 <=> a1 = a2
% Assm [h4s_indu_u_types_INJFu_u_INJ]: !f2 f1. h4/ind__type/INJF f1 = h4/ind__type/INJF f2 <=> f1 = f2
% Assm [h4s_indu_u_types_INJPu_u_INJ]: !f2_27 f2 f1_27 f1. h4/ind__type/INJP f1 f2 = h4/ind__type/INJP f1_27 f2_27 <=> f1 = f1_27 /\ f2 = f2_27
% Assm [h4s_indu_u_types_ZCONSTR0]: !r i c. h4/ind__type/ZCONSTR c i r = h4/ind__type/INJP (h4/ind__type/INJN (h4/num/SUC c)) (h4/ind__type/INJP (h4/ind__type/INJA i) (h4/ind__type/INJF r))
% Assm [h4s_indu_u_types_ZRECSPACEu_u_def]: !x. h4/ind__type/ZRECSPACE x <=> (!ZRECSPACE_27. (!a00. a00 = h4/ind__type/ZBOT \/ (?c i r. a00 = h4/ind__type/ZCONSTR c i r /\ (!n. happ ZRECSPACE_27 (happ r n))) ==> happ ZRECSPACE_27 a00) ==> happ ZRECSPACE_27 x)
% Assm [h4s_indu_u_types_recspaceu_u_repfnsu_c0]: !a. h4/ind__type/mk__rec (h4/ind__type/dest__rec a) = a
% Assm [h4s_indu_u_types_recspaceu_u_repfnsu_c1]: !r. h4/ind__type/ZRECSPACE r <=> h4/ind__type/dest__rec (h4/ind__type/mk__rec r) = r
% Assm [h4s_indu_u_types_CONSTR0]: !_0. (!r n. happ (happ _0 r) n = h4/ind__type/dest__rec (happ r n)) ==> (!r i c. h4/ind__type/CONSTR c i r = h4/ind__type/mk__rec (h4/ind__type/ZCONSTR c i (happ _0 r)))
% Assm [h4s_indu_u_types_MKu_u_RECu_u_INJ]: !y x. h4/ind__type/mk__rec x = h4/ind__type/mk__rec y ==> h4/ind__type/ZRECSPACE x /\ h4/ind__type/ZRECSPACE y ==> x = y
% Assm [h4s_indu_u_types_DESTu_u_RECu_u_INJ]: !y x. h4/ind__type/dest__rec x = h4/ind__type/dest__rec y <=> x = y
% Goal: !r2 r1 i2 i1 c2 c1. h4/ind__type/CONSTR c1 i1 r1 = h4/ind__type/CONSTR c2 i2 r2 <=> c1 = c2 /\ i1 = i2 /\ r1 = r2
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_Q253430,TV_Q253426]: ![V_f, V_g]: (![V_x]: s(TV_Q253426,happ(s(t_fun(TV_Q253430,TV_Q253426),V_f),s(TV_Q253430,V_x))) = s(TV_Q253426,happ(s(t_fun(TV_Q253430,TV_Q253426),V_g),s(TV_Q253430,V_x))) => s(t_fun(TV_Q253430,TV_Q253426),V_f) = s(t_fun(TV_Q253430,TV_Q253426),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_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_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_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_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![V_x]: 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_x))))).
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_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_ALL, 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_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_primu_u_recs_INVu_u_SUCu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_indu_u_types_INJNu_u_INJ, axiom, ![TV_u_27a]: ![V_n2, V_n1]: (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injn(s(t_h4s_nums_num,V_n1))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injn(s(t_h4s_nums_num,V_n2))) <=> s(t_h4s_nums_num,V_n1) = s(t_h4s_nums_num,V_n2))).
fof(ah4s_indu_u_types_INJAu_u_INJ, axiom, ![TV_u_27a]: ![V_a2, V_a1]: (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_inja(s(TV_u_27a,V_a1))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_inja(s(TV_u_27a,V_a2))) <=> s(TV_u_27a,V_a1) = s(TV_u_27a,V_a2))).
fof(ah4s_indu_u_types_INJFu_u_INJ, axiom, ![TV_u_27a]: ![V_f2, V_f1]: (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_f1))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_f2))) <=> s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_f1) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_f2))).
fof(ah4s_indu_u_types_INJPu_u_INJ, axiom, ![TV_u_27a]: ![V_f2u_27, V_f2, V_f1u_27, V_f1]: (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injp(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f1),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injp(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f1u_27),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2u_27))) <=> (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f1) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f1u_27) & s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2u_27)))).
fof(ah4s_indu_u_types_ZCONSTR0, axiom, ![TV_u_27a]: ![V_r, V_i, V_c]: s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_r))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injp(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injn(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_c))))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injp(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_inja(s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_r)))))))).
fof(ah4s_indu_u_types_ZRECSPACEu_u_def, axiom, ![TV_u_27a]: ![V_x]: (p(s(t_bool,h4s_indu_u_types_zrecspace(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_x)))) <=> ![V_ZRECSPACEu_27]: (![V_a00]: ((s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_a00) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zbot) | ?[V_c, V_i, V_r]: (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_a00) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_r))) & ![V_n]: p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),t_bool),V_ZRECSPACEu_27),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_r),s(t_h4s_nums_num,V_n)))))))) => p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),t_bool),V_ZRECSPACEu_27),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),t_bool),V_ZRECSPACEu_27),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_x))))))).
fof(ah4s_indu_u_types_recspaceu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_mku_u_rec(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_destu_u_rec(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a)).
fof(ah4s_indu_u_types_recspaceu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,h4s_indu_u_types_zrecspace(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_r)))) <=> s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_destu_u_rec(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_mku_u_rec(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_r))))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_r))).
fof(ah4s_indu_u_types_CONSTR0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_r, V_n]: s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_destu_u_rec(s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_r, V_i, V_c]: s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_mku_u_rec(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))))).
fof(ah4s_indu_u_types_MKu_u_RECu_u_INJ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_mku_u_rec(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_x))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_mku_u_rec(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_y))) => ((p(s(t_bool,h4s_indu_u_types_zrecspace(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_x)))) & p(s(t_bool,h4s_indu_u_types_zrecspace(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_y))))) => s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_x) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_y)))).
fof(ah4s_indu_u_types_DESTu_u_RECu_u_INJ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_destu_u_rec(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_x))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_destu_u_rec(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_y))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),V_x) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_y))).
fof(ch4s_indu_u_types_CONSTRu_u_INJ, conjecture, ![TV_u_27a]: ![V_r2, V_r1, V_i2, V_i1, V_c2, V_c1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c1),s(TV_u_27a,V_i1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r1))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c2),s(TV_u_27a,V_i2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r2))) <=> (s(t_h4s_nums_num,V_c1) = s(t_h4s_nums_num,V_c2) & (s(TV_u_27a,V_i1) = s(TV_u_27a,V_i2) & s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r1) = s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r2))))).
