%   ORIGINAL: h4/hreal/HREAL__MUL__LINV
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> 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/hrat/HRAT__MUL__SYM: !i h. h4/hrat/hrat__mul h i = h4/hrat/hrat__mul i h
% Assm: h4/hrat/HRAT__MUL__ASSOC: !j i h. h4/hrat/hrat__mul h (h4/hrat/hrat__mul i j) = h4/hrat/hrat__mul (h4/hrat/hrat__mul h i) j
% Assm: h4/hrat/HRAT__MUL__LID: !h. h4/hrat/hrat__mul h4/hrat/hrat__1 h = h
% Assm: h4/hrat/HRAT__MUL__LINV: !h. h4/hrat/hrat__mul (h4/hrat/hrat__inv h) h = h4/hrat/hrat__1
% Assm: h4/hreal/HRAT__LT__TRANS: !z y x. h4/hreal/hrat__lt x y /\ h4/hreal/hrat__lt y z ==> h4/hreal/hrat__lt x z
% Assm: h4/hreal/HRAT__MUL__RID: !x. h4/hrat/hrat__mul x h4/hrat/hrat__1 = x
% Assm: h4/hreal/HRAT__LT__LMUL: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul z x) (h4/hrat/hrat__mul z y) <=> h4/hreal/hrat__lt x y
% Assm: h4/hreal/HRAT__GT__L1: !y x. h4/hreal/hrat__lt h4/hrat/hrat__1 (h4/hrat/hrat__mul (h4/hrat/hrat__inv x) y) <=> h4/hreal/hrat__lt x y
% Assm: h4/hreal/HRAT__MEAN: !y x. h4/hreal/hrat__lt x y ==> (?z. h4/hreal/hrat__lt x z /\ h4/hreal/hrat__lt z y)
% Assm: h4/hreal/cut__of__hrat0: !x. h4/hreal/cut__of__hrat x = (\y. h4/hreal/hrat__lt y x)
% Assm: h4/hreal/hreal__tybij_c1: !r. h4/hreal/isacut r <=> h4/hreal/cut (h4/hreal/hreal0 r) = r
% Assm: h4/hreal/CUT__STRADDLE: !y x X. h4/hreal/cut X x /\ ~h4/hreal/cut X y ==> h4/hreal/hrat__lt x y
% Assm: h4/hreal/CUT__NEARTOP__MUL: !u X. h4/hreal/hrat__lt h4/hrat/hrat__1 u ==> (?x. h4/hreal/cut X x /\ ~h4/hreal/cut X (h4/hrat/hrat__mul u x))
% Assm: h4/hreal/hreal__10: h4/hreal/hreal__1 = h4/hreal/hreal0 (h4/hreal/cut__of__hrat h4/hrat/hrat__1)
% Assm: h4/hreal/hreal__mul0: !Y X. h4/hreal/hreal__mul X Y = h4/hreal/hreal0 (\w. ?x y. w = h4/hrat/hrat__mul x y /\ h4/hreal/cut X x /\ h4/hreal/cut Y y)
% Assm: h4/hreal/hreal__inv0: !X. h4/hreal/hreal__inv X = h4/hreal/hreal0 (\w. ?d. h4/hreal/hrat__lt d h4/hrat/hrat__1 /\ (!x. h4/hreal/cut X x ==> h4/hreal/hrat__lt (h4/hrat/hrat__mul w x) d))
% Assm: h4/hreal/HREAL__INV__ISACUT: !X. h4/hreal/isacut (\w. ?d. h4/hreal/hrat__lt d h4/hrat/hrat__1 /\ (!x. h4/hreal/cut X x ==> h4/hreal/hrat__lt (h4/hrat/hrat__mul w x) d))
% Goal: !X. h4/hreal/hreal__mul (h4/hreal/hreal__inv X) X = h4/hreal/hreal__1
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> 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_hrats_HRATu_u_MULu_u_SYM]: !i h. h4/hrat/hrat__mul h i = h4/hrat/hrat__mul i h
% Assm [h4s_hrats_HRATu_u_MULu_u_ASSOC]: !j i h. h4/hrat/hrat__mul h (h4/hrat/hrat__mul i j) = h4/hrat/hrat__mul (h4/hrat/hrat__mul h i) j
% Assm [h4s_hrats_HRATu_u_MULu_u_LID]: !h. h4/hrat/hrat__mul h4/hrat/hrat__1 h = h
% Assm [h4s_hrats_HRATu_u_MULu_u_LINV]: !h. h4/hrat/hrat__mul (h4/hrat/hrat__inv h) h = h4/hrat/hrat__1
% Assm [h4s_hreals_HRATu_u_LTu_u_TRANS]: !z y x. h4/hreal/hrat__lt x y /\ h4/hreal/hrat__lt y z ==> h4/hreal/hrat__lt x z
% Assm [h4s_hreals_HRATu_u_MULu_u_RID]: !x. h4/hrat/hrat__mul x h4/hrat/hrat__1 = x
% Assm [h4s_hreals_HRATu_u_LTu_u_LMUL]: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul z x) (h4/hrat/hrat__mul z y) <=> h4/hreal/hrat__lt x y
% Assm [h4s_hreals_HRATu_u_GTu_u_L1]: !y x. h4/hreal/hrat__lt h4/hrat/hrat__1 (h4/hrat/hrat__mul (h4/hrat/hrat__inv x) y) <=> h4/hreal/hrat__lt x y
% Assm [h4s_hreals_HRATu_u_MEAN]: !y x. h4/hreal/hrat__lt x y ==> (?z. h4/hreal/hrat__lt x z /\ h4/hreal/hrat__lt z y)
% Assm [h4s_hreals_cutu_u_ofu_u_hrat0]: !x x'. happ (h4/hreal/cut__of__hrat x) x' <=> h4/hreal/hrat__lt x' x
% Assm [h4s_hreals_hrealu_u_tybiju_c1]: !r. h4/hreal/isacut r <=> h4/hreal/cut (h4/hreal/hreal0 r) = r
% Assm [h4s_hreals_CUTu_u_STRADDLE]: !y x X. happ (h4/hreal/cut X) x /\ ~happ (h4/hreal/cut X) y ==> h4/hreal/hrat__lt x y
% Assm [h4s_hreals_CUTu_u_NEARTOPu_u_MUL]: !u X. h4/hreal/hrat__lt h4/hrat/hrat__1 u ==> (?x. happ (h4/hreal/cut X) x /\ ~happ (h4/hreal/cut X) (h4/hrat/hrat__mul u x))
% Assm [h4s_hreals_hrealu_u_10]: h4/hreal/hreal__1 = h4/hreal/hreal0 (h4/hreal/cut__of__hrat h4/hrat/hrat__1)
% Assm [h4s_hreals_hrealu_u_mul0]: !_0. (!X Y w. happ (happ (happ _0 X) Y) w <=> (?x y. w = h4/hrat/hrat__mul x y /\ happ (h4/hreal/cut X) x /\ happ (h4/hreal/cut Y) y)) ==> (!Y X. h4/hreal/hreal__mul X Y = h4/hreal/hreal0 (happ (happ _0 X) Y))
% Assm [h4s_hreals_hrealu_u_inv0]: !_0. (!X w. happ (happ _0 X) w <=> (?d. h4/hreal/hrat__lt d h4/hrat/hrat__1 /\ (!x. happ (h4/hreal/cut X) x ==> h4/hreal/hrat__lt (h4/hrat/hrat__mul w x) d))) ==> (!X. h4/hreal/hreal__inv X = h4/hreal/hreal0 (happ _0 X))
% Assm [h4s_hreals_HREALu_u_INVu_u_ISACUT]: !_0. (!X w. happ (happ _0 X) w <=> (?d. h4/hreal/hrat__lt d h4/hrat/hrat__1 /\ (!x. happ (h4/hreal/cut X) x ==> h4/hreal/hrat__lt (h4/hrat/hrat__mul w x) d))) ==> (!X. h4/hreal/isacut (happ _0 X))
% Goal: !X. h4/hreal/hreal__mul (h4/hreal/hreal__inv X) X = h4/hreal/hreal__1
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_Q254856,TV_Q254852]: ![V_f, V_g]: (![V_x]: s(TV_Q254852,happ(s(t_fun(TV_Q254856,TV_Q254852),V_f),s(TV_Q254856,V_x))) = s(TV_Q254852,happ(s(t_fun(TV_Q254856,TV_Q254852),V_g),s(TV_Q254856,V_x))) => s(t_fun(TV_Q254856,TV_Q254852),V_f) = s(t_fun(TV_Q254856,TV_Q254852),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> 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_hrats_HRATu_u_MULu_u_SYM, axiom, ![V_i, V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_i))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_i),s(t_h4s_hrats_hrat,V_h)))).
fof(ah4s_hrats_HRATu_u_MULu_u_ASSOC, axiom, ![V_j, V_i, V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_i),s(t_h4s_hrats_hrat,V_j))))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_i))),s(t_h4s_hrats_hrat,V_j)))).
fof(ah4s_hrats_HRATu_u_MULu_u_LID, axiom, ![V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1),s(t_h4s_hrats_hrat,V_h))) = s(t_h4s_hrats_hrat,V_h)).
fof(ah4s_hrats_HRATu_u_MULu_u_LINV, axiom, ![V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_inv(s(t_h4s_hrats_hrat,V_h))),s(t_h4s_hrats_hrat,V_h))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)).
fof(ah4s_hreals_HRATu_u_LTu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))) & p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_y),s(t_h4s_hrats_hrat,V_z))))) => p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_z)))))).
fof(ah4s_hreals_HRATu_u_MULu_u_RID, axiom, ![V_x]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1))) = s(t_h4s_hrats_hrat,V_x)).
fof(ah4s_hreals_HRATu_u_LTu_u_LMUL, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_z),s(t_h4s_hrats_hrat,V_x))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_z),s(t_h4s_hrats_hrat,V_y))))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))).
fof(ah4s_hreals_HRATu_u_GTu_u_L1, axiom, ![V_y, V_x]: s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_inv(s(t_h4s_hrats_hrat,V_x))),s(t_h4s_hrats_hrat,V_y))))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))).
fof(ah4s_hreals_HRATu_u_MEAN, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))) => ?[V_z]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_z)))) & p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_z),s(t_h4s_hrats_hrat,V_y))))))).
fof(ah4s_hreals_cutu_u_ofu_u_hrat0, axiom, ![V_x, V_xi_]: s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cutu_u_ofu_u_hrat(s(t_h4s_hrats_hrat,V_x))),s(t_h4s_hrats_hrat,V_xi_))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_xi_),s(t_h4s_hrats_hrat,V_x)))).
fof(ah4s_hreals_hrealu_u_tybiju_c1, axiom, ![V_r]: (p(s(t_bool,h4s_hreals_isacut(s(t_fun(t_h4s_hrats_hrat,t_bool),V_r)))) <=> s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,h4s_hreals_hreal0(s(t_fun(t_h4s_hrats_hrat,t_bool),V_r))))) = s(t_fun(t_h4s_hrats_hrat,t_bool),V_r))).
fof(ah4s_hreals_CUTu_u_STRADDLE, axiom, ![V_y, V_x, V_X]: ((p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_x)))) & ~ (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_y)))))) => p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))))).
fof(ah4s_hreals_CUTu_u_NEARTOPu_u_MUL, axiom, ![V_u, V_X]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1),s(t_h4s_hrats_hrat,V_u)))) => ?[V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_x)))) & ~ (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_u),s(t_h4s_hrats_hrat,V_x)))))))))).
fof(ah4s_hreals_hrealu_u_10, axiom, s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1) = s(t_h4s_hreals_hreal,h4s_hreals_hreal0(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cutu_u_ofu_u_hrat(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)))))).
fof(ah4s_hreals_hrealu_u_mul0, axiom, ![V_uu_0]: (![V_X, V_Y, V_w]: (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool)),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool))),V_uu_0),s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hreals_hreal,V_Y))),s(t_h4s_hrats_hrat,V_w)))) <=> ?[V_x, V_y]: (s(t_h4s_hrats_hrat,V_w) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y))) & (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_x)))) & p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_Y))),s(t_h4s_hrats_hrat,V_y))))))) => ![V_Y, V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,V_X),s(t_h4s_hreals_hreal,V_Y))) = s(t_h4s_hreals_hreal,h4s_hreals_hreal0(s(t_fun(t_h4s_hrats_hrat,t_bool),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool)),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool))),V_uu_0),s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hreals_hreal,V_Y))))))).
fof(ah4s_hreals_hrealu_u_inv0, axiom, ![V_uu_0]: (![V_X, V_w]: (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool)),V_uu_0),s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_w)))) <=> ?[V_d]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_d),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)))) & ![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_x)))) => p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_w),s(t_h4s_hrats_hrat,V_x))),s(t_h4s_hrats_hrat,V_d))))))) => ![V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,V_X))) = s(t_h4s_hreals_hreal,h4s_hreals_hreal0(s(t_fun(t_h4s_hrats_hrat,t_bool),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool)),V_uu_0),s(t_h4s_hreals_hreal,V_X))))))).
fof(ah4s_hreals_HREALu_u_INVu_u_ISACUT, axiom, ![V_uu_0]: (![V_X, V_w]: (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool)),V_uu_0),s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_w)))) <=> ?[V_d]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_d),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)))) & ![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hrats_hrat,V_x)))) => p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_w),s(t_h4s_hrats_hrat,V_x))),s(t_h4s_hrats_hrat,V_d))))))) => ![V_X]: p(s(t_bool,h4s_hreals_isacut(s(t_fun(t_h4s_hrats_hrat,t_bool),happ(s(t_fun(t_h4s_hreals_hreal,t_fun(t_h4s_hrats_hrat,t_bool)),V_uu_0),s(t_h4s_hreals_hreal,V_X)))))))).
fof(ch4s_hreals_HREALu_u_MULu_u_LINV, conjecture, ![V_X]: s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_mul(s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_inv(s(t_h4s_hreals_hreal,V_X))),s(t_h4s_hreals_hreal,V_X))) = s(t_h4s_hreals_hreal,h4s_hreals_hrealu_u_1)).
