%   ORIGINAL: h4/rat/RAT__RSUB__EQ
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% 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__RINV: !a. h4/rat/rat__add a (h4/rat/rat__ainv a) = h4/rat/rat__of__num h4/num/0
% 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)
% Goal: !r3 r2 r1. r1 = h4/rat/rat__sub r2 r3 <=> h4/rat/rat__add r1 r3 = 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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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_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_RINV]: !a. h4/rat/rat__add a (h4/rat/rat__ainv a) = h4/rat/rat__of__num h4/num/0
% 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)
% Goal: !r3 r2 r1. r1 = h4/rat/rat__sub r2 r3 <=> h4/rat/rat__add r1 r3 = 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_Q94354,TV_Q94350]: ![V_f, V_g]: (![V_x]: s(TV_Q94350,happ(s(t_fun(TV_Q94354,TV_Q94350),V_f),s(TV_Q94354,V_x))) = s(TV_Q94350,happ(s(t_fun(TV_Q94354,TV_Q94350),V_g),s(TV_Q94354,V_x))) => s(t_fun(TV_Q94354,TV_Q94350),V_f) = s(t_fun(TV_Q94354,TV_Q94350),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_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_RINV, 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_ainv(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_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(ch4s_rats_RATu_u_RSUBu_u_EQ, conjecture, ![V_r3, V_r2, V_r1]: (s(t_h4s_rats_rat,V_r1) = s(t_h4s_rats_rat,h4s_rats_ratu_u_sub(s(t_h4s_rats_rat,V_r2),s(t_h4s_rats_rat,V_r3))) <=> 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,V_r2))).
