%   ORIGINAL: h4/integer/INT__MOD__CALCULATE_c0
% 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/integer/INT__MOD: !n m. ~(m = h4/num/0) ==> h4/integer/int__mod (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/MOD n m)
% Goal: !n m. ~(m = h4/num/0) ==> h4/integer/int__mod (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/MOD n m)
%   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_integers_INTu_u_MOD]: !n m. ~(m = h4/num/0) ==> h4/integer/int__mod (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/MOD n m)
% Goal: !n m. ~(m = h4/num/0) ==> h4/integer/int__mod (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/MOD n m)
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_Q9702,TV_Q9698]: ![V_f, V_g]: (![V_x]: s(TV_Q9698,happ(s(t_fun(TV_Q9702,TV_Q9698),V_f),s(TV_Q9702,V_x))) = s(TV_Q9698,happ(s(t_fun(TV_Q9702,TV_Q9698),V_g),s(TV_Q9702,V_x))) => s(t_fun(TV_Q9702,TV_Q9698),V_f) = s(t_fun(TV_Q9702,TV_Q9698),V_g))).
fof(ah4s_integers_INTu_u_MOD, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)) => s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ch4s_integers_INTu_u_MODu_u_CALCULATEu_c0, conjecture, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)) => s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
