%   ORIGINAL: h4/integer/INT__EQ__LMUL2
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/integer/INT__EQ__LMUL: !z y x. h4/integer/int__mul x y = h4/integer/int__mul x z <=> x = h4/integer/int__of__num h4/num/0 \/ y = z
% Goal: !z y x. ~(x = h4/integer/int__of__num h4/num/0) ==> (y = z <=> h4/integer/int__mul x y = h4/integer/int__mul x z)
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_integers_INTu_u_EQu_u_LMUL]: !z y x. h4/integer/int__mul x y = h4/integer/int__mul x z <=> x = h4/integer/int__of__num h4/num/0 \/ y = z
% Goal: !z y x. ~(x = h4/integer/int__of__num h4/num/0) ==> (y = z <=> h4/integer/int__mul x y = h4/integer/int__mul x z)
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_Q4875,TV_Q4871]: ![V_f, V_g]: (![V_x]: s(TV_Q4871,happ(s(t_fun(TV_Q4875,TV_Q4871),V_f),s(TV_Q4875,V_x))) = s(TV_Q4871,happ(s(t_fun(TV_Q4875,TV_Q4871),V_g),s(TV_Q4875,V_x))) => s(t_fun(TV_Q4875,TV_Q4871),V_f) = s(t_fun(TV_Q4875,TV_Q4871),V_g))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_integers_INTu_u_EQu_u_LMUL, axiom, ![V_z, V_y, V_x]: (s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z))) <=> (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) | s(t_h4s_integers_int,V_y) = s(t_h4s_integers_int,V_z)))).
fof(ch4s_integers_INTu_u_EQu_u_LMUL2, conjecture, ![V_z, V_y, V_x]: (~ (s(t_h4s_integers_int,V_x) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => (s(t_h4s_integers_int,V_y) = s(t_h4s_integers_int,V_z) <=> s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_z)))))).
