%   ORIGINAL: h4/intExtension/INT__GT__RMUL__EXP
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/integer/INT__MUL__SYM: !y x. h4/integer/int__mul x y = h4/integer/int__mul y x
% Assm: h4/integer/int__gt0: !y x. h4/integer/int__gt x y <=> h4/integer/int__lt y x
% Assm: h4/integer/INT__LT__MONO: !z y x. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x ==> (h4/integer/int__lt (h4/integer/int__mul x y) (h4/integer/int__mul x z) <=> h4/integer/int__lt y z)
% Goal: !n b a. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) n ==> (h4/integer/int__gt a b <=> h4/integer/int__gt (h4/integer/int__mul a n) (h4/integer/int__mul b 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_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_integers_INTu_u_MULu_u_SYM]: !y x. h4/integer/int__mul x y = h4/integer/int__mul y x
% Assm [h4s_integers_intu_u_gt0]: !y x. h4/integer/int__gt x y <=> h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_LTu_u_MONO]: !z y x. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) x ==> (h4/integer/int__lt (h4/integer/int__mul x y) (h4/integer/int__mul x z) <=> h4/integer/int__lt y z)
% Goal: !n b a. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) n ==> (h4/integer/int__gt a b <=> h4/integer/int__gt (h4/integer/int__mul a n) (h4/integer/int__mul b 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_Q343625,TV_Q343621]: ![V_f, V_g]: (![V_x]: s(TV_Q343621,happ(s(t_fun(TV_Q343625,TV_Q343621),V_f),s(TV_Q343625,V_x))) = s(TV_Q343621,happ(s(t_fun(TV_Q343625,TV_Q343621),V_g),s(TV_Q343625,V_x))) => s(t_fun(TV_Q343625,TV_Q343621),V_f) = s(t_fun(TV_Q343625,TV_Q343621),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_integers_INTu_u_MULu_u_SYM, axiom, ![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_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_intu_u_gt0, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LTu_u_MONO, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_integers_intu_u_lt(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_x)))) => s(t_bool,h4s_integers_intu_u_lt(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_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_z))))).
fof(ch4s_intExtensions_INTu_u_GTu_u_RMULu_u_EXP, conjecture, ![V_n, V_b, V_a]: (p(s(t_bool,h4s_integers_intu_u_lt(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_n)))) => s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,V_b))) = s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_a),s(t_h4s_integers_int,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_b),s(t_h4s_integers_int,V_n))))))).
