%   ORIGINAL: h4/int__arith/justify__divides3
% 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__DIVIDES__REFL: !x. h4/integer/int__divides x x
% Assm: h4/integer/INT__DIVIDES__LMUL: !r q p. h4/integer/int__divides p q ==> h4/integer/int__divides p (h4/integer/int__mul q r)
% Assm: h4/integer/INT__DIVIDES__LADD: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add q r) <=> h4/integer/int__divides p r)
% Goal: !x n c. h4/integer/int__divides n (h4/integer/int__add (h4/integer/int__mul n x) c) <=> h4/integer/int__divides n c
%   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_DIVIDESu_u_REFL]: !x. h4/integer/int__divides x x
% Assm [h4s_integers_INTu_u_DIVIDESu_u_LMUL]: !r q p. h4/integer/int__divides p q ==> h4/integer/int__divides p (h4/integer/int__mul q r)
% Assm [h4s_integers_INTu_u_DIVIDESu_u_LADD]: !r q p. h4/integer/int__divides p q ==> (h4/integer/int__divides p (h4/integer/int__add q r) <=> h4/integer/int__divides p r)
% Goal: !x n c. h4/integer/int__divides n (h4/integer/int__add (h4/integer/int__mul n x) c) <=> h4/integer/int__divides n c
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_Q208393,TV_Q208389]: ![V_f, V_g]: (![V_x]: s(TV_Q208389,happ(s(t_fun(TV_Q208393,TV_Q208389),V_f),s(TV_Q208393,V_x))) = s(TV_Q208389,happ(s(t_fun(TV_Q208393,TV_Q208389),V_g),s(TV_Q208393,V_x))) => s(t_fun(TV_Q208393,TV_Q208389),V_f) = s(t_fun(TV_Q208393,TV_Q208389),V_g))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_x))))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_LMUL, axiom, ![V_r, V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))) => p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_r)))))))).
fof(ah4s_integers_INTu_u_DIVIDESu_u_LADD, axiom, ![V_r, V_q, V_p]: (p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_q)))) => s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,V_q),s(t_h4s_integers_int,V_r))))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_p),s(t_h4s_integers_int,V_r))))).
fof(ch4s_intu_u_ariths_justifyu_u_divides3, conjecture, ![V_x, V_n, V_c]: s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_n),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_n),s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_c))))) = s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,V_n),s(t_h4s_integers_int,V_c)))).
