%   ORIGINAL: h4/divides/ZERO__DIVIDES
% 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/TRUTH: T
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/MULT__0: !m. h4/arithmetic/_2A m h4/num/0 = h4/num/0
% Assm: h4/divides/divides__def: !b a. h4/divides/divides a b <=> (?q. b = h4/arithmetic/_2A q a)
% Goal: !m. h4/divides/divides h4/num/0 m <=> m = h4/num/0
%   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_TRUTH]: T
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_arithmetics_MULTu_u_0]: !m. h4/arithmetic/_2A m h4/num/0 = h4/num/0
% Assm [h4s_dividess_dividesu_u_def]: !b a. h4/divides/divides a b <=> (?q. b = h4/arithmetic/_2A q a)
% Goal: !m. h4/divides/divides h4/num/0 m <=> m = h4/num/0
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_Q79477,TV_Q79473]: ![V_f, V_g]: (![V_x]: s(TV_Q79473,happ(s(t_fun(TV_Q79477,TV_Q79473),V_f),s(TV_Q79477,V_x))) = s(TV_Q79473,happ(s(t_fun(TV_Q79477,TV_Q79473),V_g),s(TV_Q79477,V_x))) => s(t_fun(TV_Q79477,TV_Q79473),V_f) = s(t_fun(TV_Q79477,TV_Q79473),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EXISTSu_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_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_arithmetics_MULTu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_dividess_dividesu_u_def, axiom, ![V_b, V_a]: (p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b)))) <=> ?[V_q]: s(t_h4s_nums_num,V_b) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_q),s(t_h4s_nums_num,V_a))))).
fof(ch4s_dividess_ZEROu_u_DIVIDES, conjecture, ![V_m]: (p(s(t_bool,h4s_dividess_divides(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m)))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0))).
