%   ORIGINAL: h4/numeral/iSUB__THM_c2
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/arithmetic/ALT__ZERO: h4/arithmetic/ZERO = h4/num/0
% Assm: h4/arithmetic/BIT10: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm: h4/arithmetic/BIT20: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm: h4/arithmetic/ADD__CLAUSES_c1: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/ADD__CLAUSES_c2: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/ADD__CLAUSES_c3: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/numeral/iBIT__cases0_c0: !zf bf2 bf1. h4/numeral/iBIT__cases h4/arithmetic/ZERO zf bf1 bf2 = zf
% Assm: h4/numeral/iBIT__cases0_c1: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT1 n) zf bf1 bf2 = bf1 n
% Assm: h4/numeral/iBIT__cases0_c2: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT2 n) zf bf1 bf2 = bf2 n
% Assm: h4/numeral/iSUB__DEF_c0: !x b. h4/numeral/iSUB b h4/arithmetic/ZERO x = h4/arithmetic/ZERO
% Assm: h4/numeral/iSUB__DEF_c1: !x n b. h4/numeral/iSUB b (h4/arithmetic/BIT1 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m)) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m))) (h4/numeral/iBIT__cases x (h4/numeral/iDUB n) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) (\m. h4/numeral/iDUB (h4/numeral/iSUB F n m)))
% Assm: h4/numeral/iSUB__DEF_c2: !x n b. h4/numeral/iSUB b (h4/arithmetic/BIT2 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT2 n) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m))) (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (\m. h4/numeral/iDUB (h4/numeral/iSUB T n m)) (\m. h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)))
% Goal: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = h4/numeral/iDUB n
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_arithmetics_ALTu_u_ZERO]: h4/arithmetic/ZERO = h4/num/0
% Assm [h4s_arithmetics_BIT10]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC h4/num/0))
% Assm [h4s_arithmetics_BIT20]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/_2B n (h4/arithmetic/_2B n (h4/num/SUC (h4/num/SUC h4/num/0)))
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c1]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c2]: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c3]: !n m. h4/arithmetic/_2B m (h4/num/SUC n) = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_numerals_iBITu_u_cases0u_c0]: !zf bf2 bf1. h4/numeral/iBIT__cases h4/arithmetic/ZERO zf bf1 bf2 = zf
% Assm [h4s_numerals_iBITu_u_cases0u_c1]: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT1 n) zf bf1 bf2 = happ bf1 n
% Assm [h4s_numerals_iBITu_u_cases0u_c2]: !zf n bf2 bf1. h4/numeral/iBIT__cases (h4/arithmetic/BIT2 n) zf bf1 bf2 = happ bf2 n
% Assm [h4s_numerals_iSUBu_u_DEFu_c0]: !x b. h4/numeral/iSUB b h4/arithmetic/ZERO x = h4/arithmetic/ZERO
% Assm [h4s_numerals_iSUBu_u_DEFu_c1]: !_2. (!n m. happ (happ _2 n) m = h4/numeral/iDUB (h4/numeral/iSUB F n m)) ==> (!_1. (!n m. happ (happ _1 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) ==> (!_0. (!n m. happ (happ _0 n) m = h4/numeral/iDUB (h4/numeral/iSUB T n m)) ==> (!x n b. h4/numeral/iSUB b (h4/arithmetic/BIT1 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (happ _0 n) (happ _1 n)) (h4/numeral/iBIT__cases x (h4/numeral/iDUB n) (happ _1 n) (happ _2 n)))))
% Assm [h4s_numerals_iSUBu_u_DEFu_c2]: !_2. (!n m. happ (happ _2 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)) ==> (!_1. (!n m. happ (happ _1 n) m = h4/numeral/iDUB (h4/numeral/iSUB T n m)) ==> (!_0. (!n m. happ (happ _0 n) m = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)) ==> (!x n b. h4/numeral/iSUB b (h4/arithmetic/BIT2 n) x = h4/bool/COND b (h4/numeral/iBIT__cases x (h4/arithmetic/BIT2 n) (happ _0 n) (happ _1 n)) (h4/numeral/iBIT__cases x (h4/arithmetic/BIT1 n) (happ _1 n) (happ _2 n)))))
% Goal: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = h4/numeral/iDUB n
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_Q316607,TV_Q316603]: ![V_f, V_g]: (![V_x]: s(TV_Q316603,happ(s(t_fun(TV_Q316607,TV_Q316603),V_f),s(TV_Q316607,V_x))) = s(TV_Q316603,happ(s(t_fun(TV_Q316607,TV_Q316603),V_g),s(TV_Q316607,V_x))) => s(t_fun(TV_Q316607,TV_Q316603),V_f) = s(t_fun(TV_Q316607,TV_Q316603),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_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_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_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_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ALTu_u_ZERO, axiom, s(t_h4s_nums_num,h4s_arithmetics_zero) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_arithmetics_BIT10, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ah4s_arithmetics_BIT20, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))))))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_sucu_c0, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_iBITu_u_cases0u_c0, axiom, ![TV_u_27a]: ![V_zf, V_bf2, V_bf1]: s(TV_u_27a,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,h4s_arithmetics_zero),s(TV_u_27a,V_zf),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2))) = s(TV_u_27a,V_zf)).
fof(ah4s_numerals_iBITu_u_cases0u_c1, axiom, ![TV_u_27a]: ![V_zf, V_n, V_bf2, V_bf1]: s(TV_u_27a,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_zf),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_iBITu_u_cases0u_c2, axiom, ![TV_u_27a]: ![V_zf, V_n, V_bf2, V_bf1]: s(TV_u_27a,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_zf),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf1),s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_bf2),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_iSUBu_u_DEFu_c0, axiom, ![V_x, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_iSUBu_u_DEFu_c1, axiom, ![V_uu_2]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_1]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_0]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_x, V_n, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))))))))))).
fof(ah4s_numerals_iSUBu_u_DEFu_c2, axiom, ![V_uu_2]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_1]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_uu_0]: (![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) => ![V_x, V_n, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_numerals_ibitu_u_cases(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_1),s(t_h4s_nums_num,V_n))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),V_uu_2),s(t_h4s_nums_num,V_n))))))))))).
fof(ch4s_numerals_iSUBu_u_THMu_c2, conjecture, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n)))).
