%   ORIGINAL: h4/realax/HREAL__EQ__LADD
% 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/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/hreal/HREAL__ADD__ASSOC: !Z Y X. h4/hreal/hreal__add X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__add X Y) Z
% Assm: h4/hreal/HREAL__ADD__TOTAL: !Y X. X = Y \/ (?D. Y = h4/hreal/hreal__add X D) \/ (?D. X = h4/hreal/hreal__add Y D)
% Assm: h4/realax/HREAL__EQ__ADDR: !y x. ~(h4/hreal/hreal__add x y = x)
% Assm: h4/realax/HREAL__EQ__ADDL: !y x. ~(x = h4/hreal/hreal__add x y)
% Goal: !z y x. h4/hreal/hreal__add x y = h4/hreal/hreal__add x z <=> y = 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_TRUTH]: T
% 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_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_hreals_HREALu_u_ADDu_u_ASSOC]: !Z Y X. h4/hreal/hreal__add X (h4/hreal/hreal__add Y Z) = h4/hreal/hreal__add (h4/hreal/hreal__add X Y) Z
% Assm [h4s_hreals_HREALu_u_ADDu_u_TOTAL]: !Y X. X = Y \/ (?D. Y = h4/hreal/hreal__add X D) \/ (?D. X = h4/hreal/hreal__add Y D)
% Assm [h4s_realaxs_HREALu_u_EQu_u_ADDR]: !y x. ~(h4/hreal/hreal__add x y = x)
% Assm [h4s_realaxs_HREALu_u_EQu_u_ADDL]: !y x. ~(x = h4/hreal/hreal__add x y)
% Goal: !z y x. h4/hreal/hreal__add x y = h4/hreal/hreal__add x z <=> y = 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_Q328189,TV_Q328185]: ![V_f, V_g]: (![V_x]: s(TV_Q328185,happ(s(t_fun(TV_Q328189,TV_Q328185),V_f),s(TV_Q328189,V_x))) = s(TV_Q328185,happ(s(t_fun(TV_Q328189,TV_Q328185),V_g),s(TV_Q328189,V_x))) => s(t_fun(TV_Q328189,TV_Q328185),V_f) = s(t_fun(TV_Q328189,TV_Q328185),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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_hreals_HREALu_u_ADDu_u_ASSOC, axiom, ![V_Z, V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_Z))))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))),s(t_h4s_hreals_hreal,V_Z)))).
fof(ah4s_hreals_HREALu_u_ADDu_u_TOTAL, axiom, ![V_Y, V_X]: (s(t_h4s_hreals_hreal,V_X) = s(t_h4s_hreals_hreal,V_Y) | (?[V_D]: s(t_h4s_hreals_hreal,V_Y) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_D))) | ?[V_D]: s(t_h4s_hreals_hreal,V_X) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_Y),s(t_h4s_hreals_hreal,V_D)))))).
fof(ah4s_realaxs_HREALu_u_EQu_u_ADDR, axiom, ![V_y, V_x]: ~ (s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))) = s(t_h4s_hreals_hreal,V_x))).
fof(ah4s_realaxs_HREALu_u_EQu_u_ADDL, axiom, ![V_y, V_x]: ~ (s(t_h4s_hreals_hreal,V_x) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))))).
fof(ch4s_realaxs_HREALu_u_EQu_u_LADD, conjecture, ![V_z, V_y, V_x]: (s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_y))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_add(s(t_h4s_hreals_hreal,V_x),s(t_h4s_hreals_hreal,V_z))) <=> s(t_h4s_hreals_hreal,V_y) = s(t_h4s_hreals_hreal,V_z))).
