%   ORIGINAL: h4/rat/RAT__LES__SUB0
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/rat/RAT__ADD__ASSOC: !c b a. h4/rat/rat__add a (h4/rat/rat__add b c) = h4/rat/rat__add (h4/rat/rat__add a b) c
% Assm: h4/rat/RAT__ADD__RID: !a. h4/rat/rat__add a (h4/rat/rat__of__num h4/num/0) = a
% Assm: h4/rat/RAT__ADD__LID: !a. h4/rat/rat__add (h4/rat/rat__of__num h4/num/0) a = a
% Assm: h4/rat/RAT__ADD__LINV: !a. h4/rat/rat__add (h4/rat/rat__ainv a) a = h4/rat/rat__of__num h4/num/0
% Assm: h4/rat/RAT__SUB__ADDAINV: !r2 r1. h4/rat/rat__sub r1 r2 = h4/rat/rat__add r1 (h4/rat/rat__ainv r2)
% Assm: h4/rat/RAT__LES__RADD: !r3 r2 r1. h4/rat/rat__les (h4/rat/rat__add r1 r3) (h4/rat/rat__add r2 r3) <=> h4/rat/rat__les r1 r2
% Goal: !r2 r1. h4/rat/rat__les (h4/rat/rat__sub r1 r2) (h4/rat/rat__of__num h4/num/0) <=> h4/rat/rat__les r1 r2
%   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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_rats_RATu_u_ADDu_u_ASSOC]: !c b a. h4/rat/rat__add a (h4/rat/rat__add b c) = h4/rat/rat__add (h4/rat/rat__add a b) c
% Assm [h4s_rats_RATu_u_ADDu_u_RID]: !a. h4/rat/rat__add a (h4/rat/rat__of__num h4/num/0) = a
% Assm [h4s_rats_RATu_u_ADDu_u_LID]: !a. h4/rat/rat__add (h4/rat/rat__of__num h4/num/0) a = a
% Assm [h4s_rats_RATu_u_ADDu_u_LINV]: !a. h4/rat/rat__add (h4/rat/rat__ainv a) a = h4/rat/rat__of__num h4/num/0
% Assm [h4s_rats_RATu_u_SUBu_u_ADDAINV]: !r2 r1. h4/rat/rat__sub r1 r2 = h4/rat/rat__add r1 (h4/rat/rat__ainv r2)
% Assm [h4s_rats_RATu_u_LESu_u_RADD]: !r3 r2 r1. h4/rat/rat__les (h4/rat/rat__add r1 r3) (h4/rat/rat__add r2 r3) <=> h4/rat/rat__les r1 r2
% Goal: !r2 r1. h4/rat/rat__les (h4/rat/rat__sub r1 r2) (h4/rat/rat__of__num h4/num/0) <=> h4/rat/rat__les r1 r2
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_Q94779,TV_Q94775]: ![V_f, V_g]: (![V_x]: s(TV_Q94775,happ(s(t_fun(TV_Q94779,TV_Q94775),V_f),s(TV_Q94779,V_x))) = s(TV_Q94775,happ(s(t_fun(TV_Q94779,TV_Q94775),V_g),s(TV_Q94779,V_x))) => s(t_fun(TV_Q94779,TV_Q94775),V_f) = s(t_fun(TV_Q94779,TV_Q94775),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_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_rats_RATu_u_ADDu_u_ASSOC, axiom, ![V_c, V_b, V_a]: s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_a),s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_b),s(t_h4s_rats_rat,V_c))))) = s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_a),s(t_h4s_rats_rat,V_b))),s(t_h4s_rats_rat,V_c)))).
fof(ah4s_rats_RATu_u_ADDu_u_RID, axiom, ![V_a]: s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_a),s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_rats_rat,V_a)).
fof(ah4s_rats_RATu_u_ADDu_u_LID, axiom, ![V_a]: s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_rats_rat,V_a))) = s(t_h4s_rats_rat,V_a)).
fof(ah4s_rats_RATu_u_ADDu_u_LINV, axiom, ![V_a]: s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_a))),s(t_h4s_rats_rat,V_a))) = s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_rats_RATu_u_SUBu_u_ADDAINV, axiom, ![V_r2, V_r1]: s(t_h4s_rats_rat,h4s_rats_ratu_u_sub(s(t_h4s_rats_rat,V_r1),s(t_h4s_rats_rat,V_r2))) = s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_r1),s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r2)))))).
fof(ah4s_rats_RATu_u_LESu_u_RADD, axiom, ![V_r3, V_r2, V_r1]: s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_r1),s(t_h4s_rats_rat,V_r3))),s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,V_r2),s(t_h4s_rats_rat,V_r3))))) = s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,V_r1),s(t_h4s_rats_rat,V_r2)))).
fof(ch4s_rats_RATu_u_LESu_u_SUB0, conjecture, ![V_r2, V_r1]: s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,h4s_rats_ratu_u_sub(s(t_h4s_rats_rat,V_r1),s(t_h4s_rats_rat,V_r2))),s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,V_r1),s(t_h4s_rats_rat,V_r2)))).
