%   ORIGINAL: h4/rat/RAT__AINV__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__AINV__AINV: !r1. h4/rat/rat__ainv (h4/rat/rat__ainv r1) = r1
% Assm: h4/rat/RAT__EQ__AINV: !r2 r1. h4/rat/rat__ainv r1 = h4/rat/rat__ainv r2 <=> r1 = r2
% Goal: !r2 r1. h4/rat/rat__ainv r1 = r2 <=> r1 = h4/rat/rat__ainv 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_AINVu_u_AINV]: !r1. h4/rat/rat__ainv (h4/rat/rat__ainv r1) = r1
% Assm [h4s_rats_RATu_u_EQu_u_AINV]: !r2 r1. h4/rat/rat__ainv r1 = h4/rat/rat__ainv r2 <=> r1 = r2
% Goal: !r2 r1. h4/rat/rat__ainv r1 = r2 <=> r1 = h4/rat/rat__ainv 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_Q94304,TV_Q94300]: ![V_f, V_g]: (![V_x]: s(TV_Q94300,happ(s(t_fun(TV_Q94304,TV_Q94300),V_f),s(TV_Q94304,V_x))) = s(TV_Q94300,happ(s(t_fun(TV_Q94304,TV_Q94300),V_g),s(TV_Q94304,V_x))) => s(t_fun(TV_Q94304,TV_Q94300),V_f) = s(t_fun(TV_Q94304,TV_Q94300),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_AINVu_u_AINV, axiom, ![V_r1]: s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r1))))) = s(t_h4s_rats_rat,V_r1)).
fof(ah4s_rats_RATu_u_EQu_u_AINV, axiom, ![V_r2, V_r1]: (s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r1))) = s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r2))) <=> s(t_h4s_rats_rat,V_r1) = s(t_h4s_rats_rat,V_r2))).
fof(ch4s_rats_RATu_u_AINVu_u_EQ, conjecture, ![V_r2, V_r1]: (s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r1))) = s(t_h4s_rats_rat,V_r2) <=> s(t_h4s_rats_rat,V_r1) = s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r2))))).
