%   ORIGINAL: h4/arithmetic/ADD__MODULUS__RIGHT
% 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/arithmetic/ADD__MODULUS_c1: !x n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD (h4/arithmetic/_2B n x) n = h4/arithmetic/MOD x n
% Goal: !x n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD (h4/arithmetic/_2B n x) n = h4/arithmetic/MOD x 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_arithmetics_ADDu_u_MODULUSu_c1]: !x n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD (h4/arithmetic/_2B n x) n = h4/arithmetic/MOD x n
% Goal: !x n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD (h4/arithmetic/_2B n x) n = h4/arithmetic/MOD x 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_Q310523,TV_Q310519]: ![V_f, V_g]: (![V_x]: s(TV_Q310519,happ(s(t_fun(TV_Q310523,TV_Q310519),V_f),s(TV_Q310523,V_x))) = s(TV_Q310519,happ(s(t_fun(TV_Q310523,TV_Q310519),V_g),s(TV_Q310523,V_x))) => s(t_fun(TV_Q310523,TV_Q310519),V_f) = s(t_fun(TV_Q310523,TV_Q310519),V_g))).
fof(ah4s_arithmetics_ADDu_u_MODULUSu_c1, axiom, ![V_x, V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))))).
fof(ch4s_arithmetics_ADDu_u_MODULUSu_u_RIGHT, conjecture, ![V_x, V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_n))))).
