%   ORIGINAL: h4/integerRing/int__ring__thms_c45
% 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/integerRing/int__r__ics__aux__def: h4/integerRing/int__r__ics__aux = h4/ringNorm/r__ics__aux (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/ring/ring__accessors_c3: !f1 f0 f a0 a. h4/ring/ring__RM (h4/ring/ring0 a a0 f f0 f1) = f0
% Assm: h4/integerRing/int__r__ivl__aux__def: h4/integerRing/int__r__ivl__aux = h4/ringNorm/r__ivl__aux (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__interp__p__def: h4/integerRing/int__interp__p = h4/ringNorm/interp__p (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/ring/ring__accessors_c2: !f1 f0 f a0 a. h4/ring/ring__RP (h4/ring/ring0 a a0 f f0 f1) = f
% Assm: h4/ring/ring__accessors_c1: !f1 f0 f a0 a. h4/ring/ring__R1 (h4/ring/ring0 a a0 f f0 f1) = a0
% Assm: h4/ring/ring__accessors_c4: !f1 f0 f a0 a. h4/ring/ring__RN (h4/ring/ring0 a a0 f f0 f1) = f1
% Assm: h4/ringNorm/interp__p__def_c4: !vm r p1. h4/ringNorm/interp__p r vm (h4/ringNorm/Popp p1) = h4/ring/ring__RN r (h4/ringNorm/interp__p r vm p1)
% Assm: h4/ringNorm/interp__p__def_c0: !vm r c. h4/ringNorm/interp__p r vm (h4/ringNorm/Pconst c) = c
% Assm: h4/ringNorm/interp__p__def_c1: !vm r i. h4/ringNorm/interp__p r vm (h4/ringNorm/Pvar i) = h4/quote/varmap__find i vm
% Assm: h4/ringNorm/interp__p__def_c3: !vm r p2 p1. h4/ringNorm/interp__p r vm (h4/ringNorm/Pmult p1 p2) = h4/ring/ring__RM r (h4/ringNorm/interp__p r vm p1) (h4/ringNorm/interp__p r vm p2)
% Assm: h4/ringNorm/interp__p__def_c2: !vm r p2 p1. h4/ringNorm/interp__p r vm (h4/ringNorm/Pplus p1 p2) = h4/ring/ring__RP r (h4/ringNorm/interp__p r vm p1) (h4/ringNorm/interp__p r vm p2)
% Assm: h4/ringNorm/ivl__aux__def_c0: !x vm r. h4/ringNorm/r__ivl__aux r vm x h4/list/NIL = h4/quote/varmap__find x vm
% Assm: h4/ringNorm/ivl__aux__def_c1: !x_27 x vm t_27 r. h4/ringNorm/r__ivl__aux r vm x (h4/list/CONS x_27 t_27) = h4/ring/ring__RM r (h4/quote/varmap__find x vm) (h4/ringNorm/r__ivl__aux r vm x_27 t_27)
% Assm: h4/integerRing/int__ring__thms_c1: !vm p. h4/integerRing/int__interp__p vm p = h4/integerRing/int__r__interp__cs vm (h4/integerRing/int__polynom__simplify p)
% Assm: h4/integerRing/int__ring__thms_c43: !vm c. h4/integerRing/int__r__interp__m vm c h4/list/NIL = c
% Assm: h4/integerRing/int__ring__thms_c44: !x vm t c. h4/integerRing/int__r__interp__m vm c (h4/list/CONS x t) = h4/integer/int__mul c (h4/integerRing/int__r__ivl__aux vm x t)
% Assm: h4/integerRing/int__ring__thms_c2: !vm c. h4/integerRing/int__interp__p vm (h4/ringNorm/Pconst c) = c
% Assm: h4/integerRing/int__ring__thms_c41: !vm. h4/integerRing/int__r__interp__vl vm h4/list/NIL = h4/integer/int__1
% Assm: h4/integerRing/int__ring__thms_c4: !vm p2 p1. h4/integerRing/int__interp__p vm (h4/ringNorm/Pplus p1 p2) = h4/integer/int__add (h4/integerRing/int__interp__p vm p1) (h4/integerRing/int__interp__p vm p2)
% Assm: h4/integerRing/int__ring__thms_c42: !x vm t. h4/integerRing/int__r__interp__vl vm (h4/list/CONS x t) = h4/integerRing/int__r__ivl__aux vm x t
% Assm: h4/integerRing/int__ring__thms_c6: !vm p1. h4/integerRing/int__interp__p vm (h4/ringNorm/Popp p1) = h4/integer/int__neg (h4/integerRing/int__interp__p vm p1)
% Assm: h4/integerRing/int__ring__thms_c3: !vm i. h4/integerRing/int__interp__p vm (h4/ringNorm/Pvar i) = h4/quote/varmap__find i vm
% Assm: h4/integerRing/int__ring__thms_c39: !x vm. h4/integerRing/int__r__ivl__aux vm x h4/list/NIL = h4/quote/varmap__find x vm
% Assm: h4/integerRing/int__ring__thms_c5: !vm p2 p1. h4/integerRing/int__interp__p vm (h4/ringNorm/Pmult p1 p2) = h4/integer/int__mul (h4/integerRing/int__interp__p vm p1) (h4/integerRing/int__interp__p vm p2)
% Assm: h4/integerRing/int__ring__thms_c40: !x_27 x vm t_27. h4/integerRing/int__r__ivl__aux vm x (h4/list/CONS x_27 t_27) = h4/integer/int__mul (h4/quote/varmap__find x vm) (h4/integerRing/int__r__ivl__aux vm x_27 t_27)
% Assm: h4/ringNorm/interp__m__def_c1: !x vm t r c. h4/ringNorm/r__interp__m r vm c (h4/list/CONS x t) = h4/ring/ring__RM r c (h4/ringNorm/r__ivl__aux r vm x t)
% Assm: h4/ringNorm/interp__m__def_c0: !vm r c. h4/ringNorm/r__interp__m r vm c h4/list/NIL = c
% Assm: h4/integerRing/int__r__interp__m__def: h4/integerRing/int__r__interp__m = h4/ringNorm/r__interp__m (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__r__interp__vl__def: h4/integerRing/int__r__interp__vl = h4/ringNorm/r__interp__vl (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/ringNorm/interp__vl__def_c0: !vm r. h4/ringNorm/r__interp__vl r vm h4/list/NIL = h4/ring/ring__R1 r
% Assm: h4/ringNorm/interp__vl__def_c1: !x vm t r. h4/ringNorm/r__interp__vl r vm (h4/list/CONS x t) = h4/ringNorm/r__ivl__aux r vm x t
% Assm: h4/integerRing/int__r__interp__cs__def: h4/integerRing/int__r__interp__cs = h4/ringNorm/r__interp__cs (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/ringNorm/polynom__simplify__ok: !r. h4/ring/is__ring r ==> (!vm p. h4/ringNorm/r__interp__cs r vm (h4/ringNorm/polynom__simplify r p) = h4/ringNorm/interp__p r vm p)
% Assm: h4/integerRing/int__is__ring: h4/ring/is__ring (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__polynom__simplify__def: h4/integerRing/int__polynom__simplify = h4/ringNorm/polynom__simplify (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/canonical/ics__aux__def_c0: !vm sr a. h4/canonical/ics__aux sr vm a h4/canonical/Nil__monom = a
% Assm: h4/canonical/interp__cs__def_c0: !vm sr. h4/canonical/interp__cs sr vm h4/canonical/Nil__monom = h4/semi__ring/semi__ring__SR0 sr
% Assm: h4/ringNorm/interp__cs__def_c0: !vm r. h4/ringNorm/r__interp__cs r vm h4/canonical/Nil__monom = h4/ring/ring__R0 r
% Assm: h4/ringNorm/ics__aux__def_c0: !vm r a. h4/ringNorm/r__ics__aux r vm a h4/canonical/Nil__monom = a
% Assm: h4/integerRing/int__r__monom__insert__def: h4/integerRing/int__r__monom__insert = h4/ringNorm/r__monom__insert (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__r__canonical__sum__merge__def: h4/integerRing/int__r__canonical__sum__merge = h4/ringNorm/r__canonical__sum__merge (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__ring__thms_c20: !l1 c1. h4/integerRing/int__r__monom__insert c1 l1 h4/canonical/Nil__monom = h4/canonical/Cons__monom c1 l1 h4/canonical/Nil__monom
% Assm: h4/integerRing/int__ring__thms_c32: !l0 c0. h4/integerRing/int__r__canonical__sum__scalar3 c0 l0 h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/integerRing/int__ring__thms_c26: !c0. h4/integerRing/int__r__canonical__sum__scalar c0 h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/integerRing/int__ring__thms_c16: !v6 v5 v4. h4/integerRing/int__r__canonical__sum__merge h4/canonical/Nil__monom (h4/canonical/Cons__monom v4 v5 v6) = h4/canonical/Cons__monom v4 v5 v6
% Assm: h4/integerRing/int__ring__thms_c23: !l1. h4/integerRing/int__r__varlist__insert l1 h4/canonical/Nil__monom = h4/canonical/Cons__varlist l1 h4/canonical/Nil__monom
% Assm: h4/integerRing/int__ring__thms_c29: !l0. h4/integerRing/int__r__canonical__sum__scalar2 l0 h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/integerRing/int__ring__thms_c35: !s2. h4/integerRing/int__r__canonical__sum__prod h4/canonical/Nil__monom s2 = h4/canonical/Nil__monom
% Assm: h4/integerRing/int__ring__thms_c38: h4/integerRing/int__r__canonical__sum__simplify h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/integerRing/int__ring__thms_c17: !v8 v7. h4/integerRing/int__r__canonical__sum__merge h4/canonical/Nil__monom (h4/canonical/Cons__varlist v7 v8) = h4/canonical/Cons__varlist v7 v8
% Assm: h4/integerRing/int__ring__thms_c15: !s1. h4/integerRing/int__r__canonical__sum__merge s1 h4/canonical/Nil__monom = s1
% Assm: h4/canonical/monom__insert__tupled__primitive__def: h4/canonical/monom__insert__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!l2 c2 t2 l1 c1 sr. R (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2))) (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 (h4/canonical/Cons__monom c2 l2 t2))))) /\ (!l2 t2 l1 c1 sr. R (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2))) (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 (h4/canonical/Cons__varlist l2 t2))))))) (\monom__insert__tupled a. h4/pair/pair__CASE a (\sr v1. h4/pair/pair__CASE v1 (\c1 v3. h4/pair/pair__CASE v3 (\l1 v5. h4/canonical/canonical__sum__CASE v5 (h4/combin/I (h4/canonical/Cons__monom c1 l1 h4/canonical/Nil__monom)) (\c2 l2 t2. h4/combin/I (h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__monom c1 l1 (h4/canonical/Cons__monom c2 l2 t2)) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr c1 c2) l1 t2) (h4/canonical/Cons__monom c2 l2 (monom__insert__tupled (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2))))))) (\l2_27 t2_27. h4/combin/I (h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2_27) (h4/canonical/Cons__monom c1 l1 (h4/canonical/Cons__varlist l2_27 t2_27)) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr c1 (h4/semi__ring/semi__ring__SR1 sr)) l1 t2_27) (h4/canonical/Cons__varlist l2_27 (monom__insert__tupled (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2_27)))))))))))
% Assm: h4/canonical/canonical__sum__distinct_c1: !a1 a0. ~(h4/canonical/Nil__monom = h4/canonical/Cons__varlist a0 a1)
% Assm: h4/ring/semi__ring__of__def: !r. h4/ring/semi__ring__of r = h4/semi__ring/semi__ring0 (h4/ring/ring__R0 r) (h4/ring/ring__R1 r) (h4/ring/ring__RP r) (h4/ring/ring__RM r)
% Assm: h4/ringNorm/r__interp__vl__def: !r. h4/ringNorm/r__interp__vl r = h4/canonical/interp__vl (h4/ring/semi__ring__of r)
% Assm: h4/ringNorm/r__interp__m__def: !r. h4/ringNorm/r__interp__m r = h4/canonical/interp__m (h4/ring/semi__ring__of r)
% Assm: h4/ringNorm/r__ics__aux__def: !r. h4/ringNorm/r__ics__aux r = h4/canonical/ics__aux (h4/ring/semi__ring__of r)
% Assm: h4/integerRing/int__r__varlist__insert__def: h4/integerRing/int__r__varlist__insert = h4/ringNorm/r__varlist__insert (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__r__canonical__sum__scalar3__def: h4/integerRing/int__r__canonical__sum__scalar3 = h4/ringNorm/r__canonical__sum__scalar3 (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/ringNorm/canonical__sum__merge__def_c5: !v6 v5 v4 r. h4/ringNorm/r__canonical__sum__merge r h4/canonical/Nil__monom (h4/canonical/Cons__monom v4 v5 v6) = h4/canonical/Cons__monom v4 v5 v6
% Assm: h4/ringNorm/canonical__sum__merge__def_c4: !s1 r. h4/ringNorm/r__canonical__sum__merge r s1 h4/canonical/Nil__monom = s1
% Assm: h4/ringNorm/canonical__sum__merge__def_c0: !t2 t1 r l2 l1 c2 c1. h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__monom c1 l1 t1) (h4/canonical/Cons__monom c2 l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__monom c1 l1 (h4/ringNorm/r__canonical__sum__merge r t1 (h4/canonical/Cons__monom c2 l2 t2))) (h4/canonical/Cons__monom (h4/ring/ring__RP r c1 c2) l1 (h4/ringNorm/r__canonical__sum__merge r t1 t2)) (h4/canonical/Cons__monom c2 l2 (h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__monom c1 l1 t1) t2))
% Assm: h4/ringNorm/canonical__sum__merge__def_c1: !t2 t1 r l2 l1 c1. h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__monom c1 l1 t1) (h4/canonical/Cons__varlist l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__monom c1 l1 (h4/ringNorm/r__canonical__sum__merge r t1 (h4/canonical/Cons__varlist l2 t2))) (h4/canonical/Cons__monom (h4/ring/ring__RP r c1 (h4/ring/ring__R1 r)) l1 (h4/ringNorm/r__canonical__sum__merge r t1 t2)) (h4/canonical/Cons__varlist l2 (h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__monom c1 l1 t1) t2))
% Assm: h4/ringNorm/canonical__sum__merge__def_c2: !t2 t1 r l2 l1 c2. h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__varlist l1 t1) (h4/canonical/Cons__monom c2 l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__varlist l1 (h4/ringNorm/r__canonical__sum__merge r t1 (h4/canonical/Cons__monom c2 l2 t2))) (h4/canonical/Cons__monom (h4/ring/ring__RP r (h4/ring/ring__R1 r) c2) l1 (h4/ringNorm/r__canonical__sum__merge r t1 t2)) (h4/canonical/Cons__monom c2 l2 (h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__varlist l1 t1) t2))
% Assm: h4/ringNorm/canonical__sum__merge__def_c3: !t2 t1 r l2 l1. h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__varlist l1 t1) (h4/canonical/Cons__varlist l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__varlist l1 (h4/ringNorm/r__canonical__sum__merge r t1 (h4/canonical/Cons__varlist l2 t2))) (h4/canonical/Cons__monom (h4/ring/ring__RP r (h4/ring/ring__R1 r) (h4/ring/ring__R1 r)) l1 (h4/ringNorm/r__canonical__sum__merge r t1 t2)) (h4/canonical/Cons__varlist l2 (h4/ringNorm/r__canonical__sum__merge r (h4/canonical/Cons__varlist l1 t1) t2))
% Assm: h4/ringNorm/canonical__sum__merge__def_c6: !v8 v7 r. h4/ringNorm/r__canonical__sum__merge r h4/canonical/Nil__monom (h4/canonical/Cons__varlist v7 v8) = h4/canonical/Cons__varlist v7 v8
% Assm: h4/integerRing/int__r__canonical__sum__scalar2__def: h4/integerRing/int__r__canonical__sum__scalar2 = h4/ringNorm/r__canonical__sum__scalar2 (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/integerRing/int__r__canonical__sum__scalar__def: h4/integerRing/int__r__canonical__sum__scalar = h4/ringNorm/r__canonical__sum__scalar (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/ringNorm/canonical__sum__scalar__def_c2: !r c0. h4/ringNorm/r__canonical__sum__scalar r c0 h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/ringNorm/canonical__sum__scalar__def_c0: !t r l c0 c. h4/ringNorm/r__canonical__sum__scalar r c0 (h4/canonical/Cons__monom c l t) = h4/canonical/Cons__monom (h4/ring/ring__RM r c0 c) l (h4/ringNorm/r__canonical__sum__scalar r c0 t)
% Assm: h4/ringNorm/canonical__sum__scalar__def_c1: !t r l c0. h4/ringNorm/r__canonical__sum__scalar r c0 (h4/canonical/Cons__varlist l t) = h4/canonical/Cons__monom c0 l (h4/ringNorm/r__canonical__sum__scalar r c0 t)
% Assm: h4/ringNorm/monom__insert__def_c2: !r l1 c1. h4/ringNorm/r__monom__insert r c1 l1 h4/canonical/Nil__monom = h4/canonical/Cons__monom c1 l1 h4/canonical/Nil__monom
% Assm: h4/ringNorm/monom__insert__def_c0: !t2 r l2 l1 c2 c1. h4/ringNorm/r__monom__insert r c1 l1 (h4/canonical/Cons__monom c2 l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__monom c1 l1 (h4/canonical/Cons__monom c2 l2 t2)) (h4/canonical/Cons__monom (h4/ring/ring__RP r c1 c2) l1 t2) (h4/canonical/Cons__monom c2 l2 (h4/ringNorm/r__monom__insert r c1 l1 t2))
% Assm: h4/ringNorm/monom__insert__def_c1: !t2 r l2 l1 c1. h4/ringNorm/r__monom__insert r c1 l1 (h4/canonical/Cons__varlist l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__monom c1 l1 (h4/canonical/Cons__varlist l2 t2)) (h4/canonical/Cons__monom (h4/ring/ring__RP r c1 (h4/ring/ring__R1 r)) l1 t2) (h4/canonical/Cons__varlist l2 (h4/ringNorm/r__monom__insert r c1 l1 t2))
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/canonical/hidden____20__40ind____typecanonical2____def: h4/canonical/_20_40ind__typecanonical2 = (\a0 a1. h4/canonical/_20_40ind__typecanonical3 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB a00) (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/canonical/_20_40ind__typecanonical4 a1)))
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/canonical/canonical__sum__repfns_c1: !r. (\a0_27. !_27canonical__sum_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 a2 /\ _27canonical__sum_27 a2) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB a00) (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27canonical__sum_27 a1) ==> _27canonical__sum_27 a0_270) ==> _27canonical__sum_27 a0_27) r <=> h4/canonical/_20_40ind__typecanonical4 (h4/canonical/_20_40ind__typecanonical3 r) = r
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/canonical/hidden____20__40ind____typecanonical0____def: h4/canonical/_20_40ind__typecanonical0 = h4/canonical/_20_40ind__typecanonical3 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM))
% Assm: h4/canonical/Cons__varlist0: h4/canonical/Cons__varlist = h4/canonical/_20_40ind__typecanonical2
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/canonical/Cons__monom0: h4/canonical/Cons__monom = h4/canonical/_20_40ind__typecanonical1
% Assm: h4/canonical/Nil__monom0: h4/canonical/Nil__monom = h4/canonical/_20_40ind__typecanonical0
% Assm: h4/canonical/hidden____20__40ind____typecanonical1____def: h4/canonical/_20_40ind__typecanonical1 = (\a0 a1 a2. h4/canonical/_20_40ind__typecanonical3 ((\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 (h4/canonical/_20_40ind__typecanonical4 a2)))
% Assm: h4/canonical/canonical__sum__repfns_c0: !a. h4/canonical/_20_40ind__typecanonical3 (h4/canonical/_20_40ind__typecanonical4 a) = a
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/ringNorm/canonical__sum__scalar3__def_c2: !r l0 c0. h4/ringNorm/r__canonical__sum__scalar3 r c0 l0 h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/ringNorm/canonical__sum__scalar3__def_c1: !t r l0 l c0. h4/ringNorm/r__canonical__sum__scalar3 r c0 l0 (h4/canonical/Cons__varlist l t) = h4/ringNorm/r__monom__insert r c0 (h4/prelim/list__merge h4/quote/index__lt l0 l) (h4/ringNorm/r__canonical__sum__scalar3 r c0 l0 t)
% Assm: h4/ringNorm/canonical__sum__scalar3__def_c0: !t r l0 l c0 c. h4/ringNorm/r__canonical__sum__scalar3 r c0 l0 (h4/canonical/Cons__monom c l t) = h4/ringNorm/r__monom__insert r (h4/ring/ring__RM r c0 c) (h4/prelim/list__merge h4/quote/index__lt l0 l) (h4/ringNorm/r__canonical__sum__scalar3 r c0 l0 t)
% Assm: h4/canonical/ics__aux__def_c2: !vm t sr l c a. h4/canonical/ics__aux sr vm a (h4/canonical/Cons__monom c l t) = h4/semi__ring/semi__ring__SRP sr a (h4/canonical/ics__aux sr vm (h4/canonical/interp__m sr vm c l) t)
% Assm: h4/canonical/ics__aux__def_c1: !vm t sr l a. h4/canonical/ics__aux sr vm a (h4/canonical/Cons__varlist l t) = h4/semi__ring/semi__ring__SRP sr a (h4/canonical/ics__aux sr vm (h4/canonical/interp__vl sr vm l) t)
% Assm: h4/semi__ring/semi__ring__accessors_c2: !f0 f a0 a. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring0 a a0 f f0) = f
% Assm: h4/ringNorm/r__interp__cs__def: !r. h4/ringNorm/r__interp__cs r = h4/canonical/interp__cs (h4/ring/semi__ring__of r)
% Assm: h4/canonical/interp__cs__def_c2: !vm t sr l c. h4/canonical/interp__cs sr vm (h4/canonical/Cons__monom c l t) = h4/canonical/ics__aux sr vm (h4/canonical/interp__m sr vm c l) t
% Assm: h4/canonical/interp__cs__def_c1: !vm t sr l. h4/canonical/interp__cs sr vm (h4/canonical/Cons__varlist l t) = h4/canonical/ics__aux sr vm (h4/canonical/interp__vl sr vm l) t
% Assm: h4/semi__ring/semi__ring__accessors_c0: !f0 f a0 a. h4/semi__ring/semi__ring__SR0 (h4/semi__ring/semi__ring0 a a0 f f0) = a
% Assm: h4/ringNorm/varlist__insert__def_c2: !r l1. h4/ringNorm/r__varlist__insert r l1 h4/canonical/Nil__monom = h4/canonical/Cons__varlist l1 h4/canonical/Nil__monom
% Assm: h4/ringNorm/varlist__insert__def_c1: !t2 r l2 l1. h4/ringNorm/r__varlist__insert r l1 (h4/canonical/Cons__varlist l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__varlist l1 (h4/canonical/Cons__varlist l2 t2)) (h4/canonical/Cons__monom (h4/ring/ring__RP r (h4/ring/ring__R1 r) (h4/ring/ring__R1 r)) l1 t2) (h4/canonical/Cons__varlist l2 (h4/ringNorm/r__varlist__insert r l1 t2))
% Assm: h4/ringNorm/varlist__insert__def_c0: !t2 r l2 l1 c2. h4/ringNorm/r__varlist__insert r l1 (h4/canonical/Cons__monom c2 l2 t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (h4/canonical/Cons__varlist l1 (h4/canonical/Cons__monom c2 l2 t2)) (h4/canonical/Cons__monom (h4/ring/ring__RP r (h4/ring/ring__R1 r) c2) l1 t2) (h4/canonical/Cons__monom c2 l2 (h4/ringNorm/r__varlist__insert r l1 t2))
% Assm: h4/ringNorm/canonical__sum__scalar2__def_c1: !t r l0 l. h4/ringNorm/r__canonical__sum__scalar2 r l0 (h4/canonical/Cons__varlist l t) = h4/ringNorm/r__varlist__insert r (h4/prelim/list__merge h4/quote/index__lt l0 l) (h4/ringNorm/r__canonical__sum__scalar2 r l0 t)
% Assm: h4/ringNorm/canonical__sum__scalar2__def_c0: !t r l0 l c. h4/ringNorm/r__canonical__sum__scalar2 r l0 (h4/canonical/Cons__monom c l t) = h4/ringNorm/r__monom__insert r c (h4/prelim/list__merge h4/quote/index__lt l0 l) (h4/ringNorm/r__canonical__sum__scalar2 r l0 t)
% Assm: h4/ringNorm/canonical__sum__scalar2__def_c2: !r l0. h4/ringNorm/r__canonical__sum__scalar2 r l0 h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/integerRing/int__r__canonical__sum__simplify__def: h4/integerRing/int__r__canonical__sum__simplify = h4/ringNorm/r__canonical__sum__simplify (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/ringNorm/canonical__sum__simplify__def_c2: !r. h4/ringNorm/r__canonical__sum__simplify r h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm: h4/ringNorm/canonical__sum__simplify__def_c0: !t r l c. h4/ringNorm/r__canonical__sum__simplify r (h4/canonical/Cons__monom c l t) = h4/bool/COND (c = h4/ring/ring__R0 r) (h4/ringNorm/r__canonical__sum__simplify r t) (h4/bool/COND (c = h4/ring/ring__R1 r) (h4/canonical/Cons__varlist l (h4/ringNorm/r__canonical__sum__simplify r t)) (h4/canonical/Cons__monom c l (h4/ringNorm/r__canonical__sum__simplify r t)))
% Assm: h4/ringNorm/canonical__sum__simplify__def_c1: !t r l. h4/ringNorm/r__canonical__sum__simplify r (h4/canonical/Cons__varlist l t) = h4/canonical/Cons__varlist l (h4/ringNorm/r__canonical__sum__simplify r t)
% Assm: h4/ring/ring__accessors_c0: !f1 f0 f a0 a. h4/ring/ring__R0 (h4/ring/ring0 a a0 f f0 f1) = a
% Assm: h4/integerRing/int__r__canonical__sum__prod__def: h4/integerRing/int__r__canonical__sum__prod = h4/ringNorm/r__canonical__sum__prod (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm: h4/ringNorm/canonical__sum__prod__def_c2: !s2 r. h4/ringNorm/r__canonical__sum__prod r h4/canonical/Nil__monom s2 = h4/canonical/Nil__monom
% Assm: h4/ringNorm/canonical__sum__prod__def_c1: !t1 s2 r l1. h4/ringNorm/r__canonical__sum__prod r (h4/canonical/Cons__varlist l1 t1) s2 = h4/ringNorm/r__canonical__sum__merge r (h4/ringNorm/r__canonical__sum__scalar2 r l1 s2) (h4/ringNorm/r__canonical__sum__prod r t1 s2)
% Assm: h4/ringNorm/canonical__sum__prod__def_c0: !t1 s2 r l1 c1. h4/ringNorm/r__canonical__sum__prod r (h4/canonical/Cons__monom c1 l1 t1) s2 = h4/ringNorm/r__canonical__sum__merge r (h4/ringNorm/r__canonical__sum__scalar3 r c1 l1 s2) (h4/ringNorm/r__canonical__sum__prod r t1 s2)
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Goal: !vm a. h4/integerRing/int__r__ics__aux vm a h4/canonical/Nil__monom = a
%   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_integerRings_intu_u_ru_u_icsu_u_auxu_u_def]: h4/integerRing/int__r__ics__aux = h4/ringNorm/r__ics__aux (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_rings_ringu_u_accessorsu_c3]: !f1 f0 f a0 a. h4/ring/ring__RM (h4/ring/ring0 a a0 f f0 f1) = f0
% Assm [h4s_integerRings_intu_u_ru_u_ivlu_u_auxu_u_def]: h4/integerRing/int__r__ivl__aux = h4/ringNorm/r__ivl__aux (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_interpu_u_pu_u_def]: h4/integerRing/int__interp__p = h4/ringNorm/interp__p (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_rings_ringu_u_accessorsu_c2]: !f1 f0 f a0 a. h4/ring/ring__RP (h4/ring/ring0 a a0 f f0 f1) = f
% Assm [h4s_rings_ringu_u_accessorsu_c1]: !f1 f0 f a0 a. h4/ring/ring__R1 (h4/ring/ring0 a a0 f f0 f1) = a0
% Assm [h4s_rings_ringu_u_accessorsu_c4]: !f1 f0 f a0 a. h4/ring/ring__RN (h4/ring/ring0 a a0 f f0 f1) = f1
% Assm [h4s_ringNorms_interpu_u_pu_u_defu_c4]: !vm r p1. happ (happ (h4/ringNorm/interp__p r) vm) (h4/ringNorm/Popp p1) = happ (h4/ring/ring__RN r) (happ (happ (h4/ringNorm/interp__p r) vm) p1)
% Assm [h4s_ringNorms_interpu_u_pu_u_defu_c0]: !vm r c. happ (happ (h4/ringNorm/interp__p r) vm) (h4/ringNorm/Pconst c) = c
% Assm [h4s_ringNorms_interpu_u_pu_u_defu_c1]: !vm r i. happ (happ (h4/ringNorm/interp__p r) vm) (h4/ringNorm/Pvar i) = h4/quote/varmap__find i vm
% Assm [h4s_ringNorms_interpu_u_pu_u_defu_c3]: !vm r p2 p1. happ (happ (h4/ringNorm/interp__p r) vm) (h4/ringNorm/Pmult p1 p2) = happ (happ (h4/ring/ring__RM r) (happ (happ (h4/ringNorm/interp__p r) vm) p1)) (happ (happ (h4/ringNorm/interp__p r) vm) p2)
% Assm [h4s_ringNorms_interpu_u_pu_u_defu_c2]: !vm r p2 p1. happ (happ (h4/ringNorm/interp__p r) vm) (h4/ringNorm/Pplus p1 p2) = happ (happ (h4/ring/ring__RP r) (happ (happ (h4/ringNorm/interp__p r) vm) p1)) (happ (happ (h4/ringNorm/interp__p r) vm) p2)
% Assm [h4s_ringNorms_ivlu_u_auxu_u_defu_c0]: !x vm r. happ (happ (happ (h4/ringNorm/r__ivl__aux r) vm) x) h4/list/NIL = h4/quote/varmap__find x vm
% Assm [h4s_ringNorms_ivlu_u_auxu_u_defu_c1]: !x_27 x vm t_27 r. happ (happ (happ (h4/ringNorm/r__ivl__aux r) vm) x) (h4/list/CONS x_27 t_27) = happ (happ (h4/ring/ring__RM r) (h4/quote/varmap__find x vm)) (happ (happ (happ (h4/ringNorm/r__ivl__aux r) vm) x_27) t_27)
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c1]: !vm p. happ (happ h4/integerRing/int__interp__p vm) p = happ (happ h4/integerRing/int__r__interp__cs vm) (happ h4/integerRing/int__polynom__simplify p)
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c43]: !vm c. happ (happ (happ h4/integerRing/int__r__interp__m vm) c) h4/list/NIL = c
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c44]: !x vm t c. happ (happ (happ h4/integerRing/int__r__interp__m vm) c) (h4/list/CONS x t) = happ (happ h4/integer/int__mul c) (happ (happ (happ h4/integerRing/int__r__ivl__aux vm) x) t)
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c2]: !vm c. happ (happ h4/integerRing/int__interp__p vm) (h4/ringNorm/Pconst c) = c
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c41]: !vm. happ (happ h4/integerRing/int__r__interp__vl vm) h4/list/NIL = h4/integer/int__1
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c4]: !vm p2 p1. happ (happ h4/integerRing/int__interp__p vm) (h4/ringNorm/Pplus p1 p2) = happ (happ h4/integer/int__add (happ (happ h4/integerRing/int__interp__p vm) p1)) (happ (happ h4/integerRing/int__interp__p vm) p2)
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c42]: !x vm t. happ (happ h4/integerRing/int__r__interp__vl vm) (h4/list/CONS x t) = happ (happ (happ h4/integerRing/int__r__ivl__aux vm) x) t
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c6]: !vm p1. happ (happ h4/integerRing/int__interp__p vm) (h4/ringNorm/Popp p1) = happ h4/integer/int__neg (happ (happ h4/integerRing/int__interp__p vm) p1)
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c3]: !vm i. happ (happ h4/integerRing/int__interp__p vm) (h4/ringNorm/Pvar i) = h4/quote/varmap__find i vm
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c39]: !x vm. happ (happ (happ h4/integerRing/int__r__ivl__aux vm) x) h4/list/NIL = h4/quote/varmap__find x vm
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c5]: !vm p2 p1. happ (happ h4/integerRing/int__interp__p vm) (h4/ringNorm/Pmult p1 p2) = happ (happ h4/integer/int__mul (happ (happ h4/integerRing/int__interp__p vm) p1)) (happ (happ h4/integerRing/int__interp__p vm) p2)
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c40]: !x_27 x vm t_27. happ (happ (happ h4/integerRing/int__r__ivl__aux vm) x) (h4/list/CONS x_27 t_27) = happ (happ h4/integer/int__mul (h4/quote/varmap__find x vm)) (happ (happ (happ h4/integerRing/int__r__ivl__aux vm) x_27) t_27)
% Assm [h4s_ringNorms_interpu_u_mu_u_defu_c1]: !x vm t r c. happ (happ (happ (h4/ringNorm/r__interp__m r) vm) c) (h4/list/CONS x t) = happ (happ (h4/ring/ring__RM r) c) (happ (happ (happ (h4/ringNorm/r__ivl__aux r) vm) x) t)
% Assm [h4s_ringNorms_interpu_u_mu_u_defu_c0]: !vm r c. happ (happ (happ (h4/ringNorm/r__interp__m r) vm) c) h4/list/NIL = c
% Assm [h4s_integerRings_intu_u_ru_u_interpu_u_mu_u_def]: h4/integerRing/int__r__interp__m = h4/ringNorm/r__interp__m (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ru_u_interpu_u_vlu_u_def]: h4/integerRing/int__r__interp__vl = h4/ringNorm/r__interp__vl (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_ringNorms_interpu_u_vlu_u_defu_c0]: !vm r. happ (happ (h4/ringNorm/r__interp__vl r) vm) h4/list/NIL = h4/ring/ring__R1 r
% Assm [h4s_ringNorms_interpu_u_vlu_u_defu_c1]: !x vm t r. happ (happ (h4/ringNorm/r__interp__vl r) vm) (h4/list/CONS x t) = happ (happ (happ (h4/ringNorm/r__ivl__aux r) vm) x) t
% Assm [h4s_integerRings_intu_u_ru_u_interpu_u_csu_u_def]: h4/integerRing/int__r__interp__cs = h4/ringNorm/r__interp__cs (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_ringNorms_polynomu_u_simplifyu_u_ok]: !r. h4/ring/is__ring r ==> (!vm p. happ (happ (h4/ringNorm/r__interp__cs r) vm) (happ (h4/ringNorm/polynom__simplify r) p) = happ (happ (h4/ringNorm/interp__p r) vm) p)
% Assm [h4s_integerRings_intu_u_isu_u_ring]: h4/ring/is__ring (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_polynomu_u_simplifyu_u_def]: h4/integerRing/int__polynom__simplify = h4/ringNorm/polynom__simplify (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_canonicals_icsu_u_auxu_u_defu_c0]: !vm sr a. happ (happ (happ (h4/canonical/ics__aux sr) vm) a) h4/canonical/Nil__monom = a
% Assm [h4s_canonicals_interpu_u_csu_u_defu_c0]: !vm sr. happ (happ (h4/canonical/interp__cs sr) vm) h4/canonical/Nil__monom = h4/semi__ring/semi__ring__SR0 sr
% Assm [h4s_ringNorms_interpu_u_csu_u_defu_c0]: !vm r. happ (happ (h4/ringNorm/r__interp__cs r) vm) h4/canonical/Nil__monom = h4/ring/ring__R0 r
% Assm [h4s_ringNorms_icsu_u_auxu_u_defu_c0]: !vm r a. happ (happ (happ (h4/ringNorm/r__ics__aux r) vm) a) h4/canonical/Nil__monom = a
% Assm [h4s_integerRings_intu_u_ru_u_monomu_u_insertu_u_def]: h4/integerRing/int__r__monom__insert = h4/ringNorm/r__monom__insert (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def]: h4/integerRing/int__r__canonical__sum__merge = h4/ringNorm/r__canonical__sum__merge (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c20]: !l1 c1. happ (happ (happ h4/integerRing/int__r__monom__insert c1) l1) h4/canonical/Nil__monom = happ (happ (happ h4/canonical/Cons__monom c1) l1) h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c32]: !l0 c0. happ (happ (happ h4/integerRing/int__r__canonical__sum__scalar3 c0) l0) h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c26]: !c0. happ (happ h4/integerRing/int__r__canonical__sum__scalar c0) h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c16]: !v6 v5 v4. happ (happ h4/integerRing/int__r__canonical__sum__merge h4/canonical/Nil__monom) (happ (happ (happ h4/canonical/Cons__monom v4) v5) v6) = happ (happ (happ h4/canonical/Cons__monom v4) v5) v6
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c23]: !l1. happ (happ h4/integerRing/int__r__varlist__insert l1) h4/canonical/Nil__monom = happ (happ h4/canonical/Cons__varlist l1) h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c29]: !l0. happ (happ h4/integerRing/int__r__canonical__sum__scalar2 l0) h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c35]: !s2. happ (happ h4/integerRing/int__r__canonical__sum__prod h4/canonical/Nil__monom) s2 = h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c38]: happ h4/integerRing/int__r__canonical__sum__simplify h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c17]: !v8 v7. happ (happ h4/integerRing/int__r__canonical__sum__merge h4/canonical/Nil__monom) (happ (happ h4/canonical/Cons__varlist v7) v8) = happ (happ h4/canonical/Cons__varlist v7) v8
% Assm [h4s_integerRings_intu_u_ringu_u_thmsu_c15]: !s1. happ (happ h4/integerRing/int__r__canonical__sum__merge s1) h4/canonical/Nil__monom = s1
% Assm [h4s_canonicals_monomu_u_insertu_u_tupledu_u_primitiveu_u_def]: !_13. (!l2_27 monom__insert__tupled sr c1 l1 t2_27. happ (happ (happ (happ (happ (happ _13 l2_27) monom__insert__tupled) sr) c1) l1) t2_27 = h4/combin/I (h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2_27) (happ (happ (happ h4/canonical/Cons__monom c1) l1) (happ (happ h4/canonical/Cons__varlist l2_27) t2_27)) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/semi__ring/semi__ring__SRP sr) c1) (h4/semi__ring/semi__ring__SR1 sr))) l1) t2_27) (happ (happ h4/canonical/Cons__varlist l2_27) (happ monom__insert__tupled (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2_27))))))) ==> (!_12. (!monom__insert__tupled sr c1 l1 l2_27. happ (happ (happ (happ (happ _12 monom__insert__tupled) sr) c1) l1) l2_27 = happ (happ (happ (happ (happ _13 l2_27) monom__insert__tupled) sr) c1) l1) ==> (!_11. (!c2 l2 monom__insert__tupled sr c1 l1 t2. happ (happ (happ (happ (happ (happ (happ _11 c2) l2) monom__insert__tupled) sr) c1) l1) t2 = h4/combin/I (h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ (happ h4/canonical/Cons__monom c1) l1) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2)) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/semi__ring/semi__ring__SRP sr) c1) c2)) l1) t2) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ monom__insert__tupled (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2))))))) ==> (!_10. (!c2 monom__insert__tupled sr c1 l1 l2. happ (happ (happ (happ (happ (happ _10 c2) monom__insert__tupled) sr) c1) l1) l2 = happ (happ (happ (happ (happ (happ _11 c2) l2) monom__insert__tupled) sr) c1) l1) ==> (!_9. (!monom__insert__tupled sr c1 l1 c2. happ (happ (happ (happ (happ _9 monom__insert__tupled) sr) c1) l1) c2 = happ (happ (happ (happ (happ _10 c2) monom__insert__tupled) sr) c1) l1) ==> (!_8. (!monom__insert__tupled sr c1 l1 v5. happ (happ (happ (happ (happ _8 monom__insert__tupled) sr) c1) l1) v5 = h4/canonical/canonical__sum__CASE v5 (h4/combin/I (happ (happ (happ h4/canonical/Cons__monom c1) l1) h4/canonical/Nil__monom)) (happ (happ (happ (happ _9 monom__insert__tupled) sr) c1) l1) (happ (happ (happ (happ _12 monom__insert__tupled) sr) c1) l1)) ==> (!_7. (!monom__insert__tupled sr c1 l1. happ (happ (happ (happ _7 monom__insert__tupled) sr) c1) l1 = happ (happ (happ (happ _8 monom__insert__tupled) sr) c1) l1) ==> (!_6. (!monom__insert__tupled sr c1 v3. happ (happ (happ (happ _6 monom__insert__tupled) sr) c1) v3 = h4/pair/pair__CASE v3 (happ (happ (happ _7 monom__insert__tupled) sr) c1)) ==> (!_5. (!monom__insert__tupled sr c1. happ (happ (happ _5 monom__insert__tupled) sr) c1 = happ (happ (happ _6 monom__insert__tupled) sr) c1) ==> (!_4. (!monom__insert__tupled sr v1. happ (happ (happ _4 monom__insert__tupled) sr) v1 = h4/pair/pair__CASE v1 (happ (happ _5 monom__insert__tupled) sr)) ==> (!_3. (!monom__insert__tupled sr. happ (happ _3 monom__insert__tupled) sr = happ (happ _4 monom__insert__tupled) sr) ==> (!_2. (!monom__insert__tupled a. happ (happ _2 monom__insert__tupled) a = h4/pair/pair__CASE a (happ _3 monom__insert__tupled)) ==> (!_1. (!monom__insert__tupled. happ _1 monom__insert__tupled = happ _2 monom__insert__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!l2 c2 t2 l1 c1 sr. happ (happ R (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2)))) (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2))))) /\ (!l2 t2 l1 c1 sr. happ (happ R (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 t2)))) (h4/pair/_2C sr (h4/pair/_2C c1 (h4/pair/_2C l1 (happ (happ h4/canonical/Cons__varlist l2) t2)))))) ==> h4/canonical/monom__insert__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))))))
% Assm [h4s_canonicals_canonicalu_u_sumu_u_distinctu_c1]: !a1 a0. ~(h4/canonical/Nil__monom = happ (happ h4/canonical/Cons__varlist a0) a1)
% Assm [h4s_rings_semiu_u_ringu_u_ofu_u_def]: !r. h4/ring/semi__ring__of r = h4/semi__ring/semi__ring0 (h4/ring/ring__R0 r) (h4/ring/ring__R1 r) (h4/ring/ring__RP r) (h4/ring/ring__RM r)
% Assm [h4s_ringNorms_ru_u_interpu_u_vlu_u_def]: !r. h4/ringNorm/r__interp__vl r = h4/canonical/interp__vl (h4/ring/semi__ring__of r)
% Assm [h4s_ringNorms_ru_u_interpu_u_mu_u_def]: !r. h4/ringNorm/r__interp__m r = h4/canonical/interp__m (h4/ring/semi__ring__of r)
% Assm [h4s_ringNorms_ru_u_icsu_u_auxu_u_def]: !r. h4/ringNorm/r__ics__aux r = h4/canonical/ics__aux (h4/ring/semi__ring__of r)
% Assm [h4s_integerRings_intu_u_ru_u_varlistu_u_insertu_u_def]: h4/integerRing/int__r__varlist__insert = h4/ringNorm/r__varlist__insert (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3u_u_def]: h4/integerRing/int__r__canonical__sum__scalar3 = h4/ringNorm/r__canonical__sum__scalar3 (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c5]: !v6 v5 v4 r. happ (happ (h4/ringNorm/r__canonical__sum__merge r) h4/canonical/Nil__monom) (happ (happ (happ h4/canonical/Cons__monom v4) v5) v6) = happ (happ (happ h4/canonical/Cons__monom v4) v5) v6
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c4]: !s1 r. happ (happ (h4/ringNorm/r__canonical__sum__merge r) s1) h4/canonical/Nil__monom = s1
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c0]: !t2 t1 r l2 l1 c2 c1. happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ (happ h4/canonical/Cons__monom c1) l1) t1)) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ (happ h4/canonical/Cons__monom c1) l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2))) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) c1) c2)) l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) t2)) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ (happ h4/canonical/Cons__monom c1) l1) t1)) t2))
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c1]: !t2 t1 r l2 l1 c1. happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ (happ h4/canonical/Cons__monom c1) l1) t1)) (happ (happ h4/canonical/Cons__varlist l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ (happ h4/canonical/Cons__monom c1) l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) (happ (happ h4/canonical/Cons__varlist l2) t2))) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) c1) (h4/ring/ring__R1 r))) l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) t2)) (happ (happ h4/canonical/Cons__varlist l2) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ (happ h4/canonical/Cons__monom c1) l1) t1)) t2))
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c2]: !t2 t1 r l2 l1 c2. happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ h4/canonical/Cons__varlist l1) t1)) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ h4/canonical/Cons__varlist l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2))) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) (h4/ring/ring__R1 r)) c2)) l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) t2)) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ h4/canonical/Cons__varlist l1) t1)) t2))
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c3]: !t2 t1 r l2 l1. happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ h4/canonical/Cons__varlist l1) t1)) (happ (happ h4/canonical/Cons__varlist l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ h4/canonical/Cons__varlist l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) (happ (happ h4/canonical/Cons__varlist l2) t2))) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) (h4/ring/ring__R1 r)) (h4/ring/ring__R1 r))) l1) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) t1) t2)) (happ (happ h4/canonical/Cons__varlist l2) (happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ h4/canonical/Cons__varlist l1) t1)) t2))
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c6]: !v8 v7 r. happ (happ (h4/ringNorm/r__canonical__sum__merge r) h4/canonical/Nil__monom) (happ (happ h4/canonical/Cons__varlist v7) v8) = happ (happ h4/canonical/Cons__varlist v7) v8
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalar2u_u_def]: h4/integerRing/int__r__canonical__sum__scalar2 = h4/ringNorm/r__canonical__sum__scalar2 (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalaru_u_def]: h4/integerRing/int__r__canonical__sum__scalar = h4/ringNorm/r__canonical__sum__scalar (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c2]: !r c0. happ (happ (h4/ringNorm/r__canonical__sum__scalar r) c0) h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c0]: !t r l c0 c. happ (happ (h4/ringNorm/r__canonical__sum__scalar r) c0) (happ (happ (happ h4/canonical/Cons__monom c) l) t) = happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RM r) c0) c)) l) (happ (happ (h4/ringNorm/r__canonical__sum__scalar r) c0) t)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c1]: !t r l c0. happ (happ (h4/ringNorm/r__canonical__sum__scalar r) c0) (happ (happ h4/canonical/Cons__varlist l) t) = happ (happ (happ h4/canonical/Cons__monom c0) l) (happ (happ (h4/ringNorm/r__canonical__sum__scalar r) c0) t)
% Assm [h4s_ringNorms_monomu_u_insertu_u_defu_c2]: !r l1 c1. happ (happ (happ (h4/ringNorm/r__monom__insert r) c1) l1) h4/canonical/Nil__monom = happ (happ (happ h4/canonical/Cons__monom c1) l1) h4/canonical/Nil__monom
% Assm [h4s_ringNorms_monomu_u_insertu_u_defu_c0]: !t2 r l2 l1 c2 c1. happ (happ (happ (h4/ringNorm/r__monom__insert r) c1) l1) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ (happ h4/canonical/Cons__monom c1) l1) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2)) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) c1) c2)) l1) t2) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ (happ (happ (h4/ringNorm/r__monom__insert r) c1) l1) t2))
% Assm [h4s_ringNorms_monomu_u_insertu_u_defu_c1]: !t2 r l2 l1 c1. happ (happ (happ (h4/ringNorm/r__monom__insert r) c1) l1) (happ (happ h4/canonical/Cons__varlist l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ (happ h4/canonical/Cons__monom c1) l1) (happ (happ h4/canonical/Cons__varlist l2) t2)) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) c1) (h4/ring/ring__R1 r))) l1) t2) (happ (happ h4/canonical/Cons__varlist l2) (happ (happ (happ (h4/ringNorm/r__monom__insert r) c1) l1) t2))
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/canonical/_20_40ind__typecanonical2 x) x = h4/canonical/_20_40ind__typecanonical3 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB x) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical4 x) _0)))
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_canonicals_canonicalu_u_sumu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27canonical__sum_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _0 \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C a0 a1) (h4/ind__type/FCONS a2 _0) /\ happ _27canonical__sum_27 a2) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB a0) (h4/ind__type/FCONS a1 _0) /\ happ _27canonical__sum_27 a1) ==> happ _27canonical__sum_27 a0_270) ==> happ _27canonical__sum_27 r) <=> h4/canonical/_20_40ind__typecanonical4 (h4/canonical/_20_40ind__typecanonical3 r) = r)
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/canonical/_20_40ind__typecanonical0 = h4/canonical/_20_40ind__typecanonical3 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _0)
% Assm [h4s_canonicals_Consu_u_varlist0]: h4/canonical/Cons__varlist = h4/canonical/_20_40ind__typecanonical2
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_canonicals_Consu_u_monom0]: h4/canonical/Cons__monom = h4/canonical/_20_40ind__typecanonical1
% Assm [h4s_canonicals_Nilu_u_monom0]: h4/canonical/Nil__monom = h4/canonical/_20_40ind__typecanonical0
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x x. happ (happ (happ h4/canonical/_20_40ind__typecanonical1 x) x) x = h4/canonical/_20_40ind__typecanonical3 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C x x) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical4 x) _0)))
% Assm [h4s_canonicals_canonicalu_u_sumu_u_repfnsu_c0]: !a. h4/canonical/_20_40ind__typecanonical3 (h4/canonical/_20_40ind__typecanonical4 a) = a
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalar3u_u_defu_c2]: !r l0 c0. happ (happ (happ (h4/ringNorm/r__canonical__sum__scalar3 r) c0) l0) h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalar3u_u_defu_c1]: !t r l0 l c0. happ (happ (happ (h4/ringNorm/r__canonical__sum__scalar3 r) c0) l0) (happ (happ h4/canonical/Cons__varlist l) t) = happ (happ (happ (h4/ringNorm/r__monom__insert r) c0) (h4/prelim/list__merge h4/quote/index__lt l0 l)) (happ (happ (happ (h4/ringNorm/r__canonical__sum__scalar3 r) c0) l0) t)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalar3u_u_defu_c0]: !t r l0 l c0 c. happ (happ (happ (h4/ringNorm/r__canonical__sum__scalar3 r) c0) l0) (happ (happ (happ h4/canonical/Cons__monom c) l) t) = happ (happ (happ (h4/ringNorm/r__monom__insert r) (happ (happ (h4/ring/ring__RM r) c0) c)) (h4/prelim/list__merge h4/quote/index__lt l0 l)) (happ (happ (happ (h4/ringNorm/r__canonical__sum__scalar3 r) c0) l0) t)
% Assm [h4s_canonicals_icsu_u_auxu_u_defu_c2]: !vm t sr l c a. happ (happ (happ (h4/canonical/ics__aux sr) vm) a) (happ (happ (happ h4/canonical/Cons__monom c) l) t) = happ (happ (h4/semi__ring/semi__ring__SRP sr) a) (happ (happ (happ (h4/canonical/ics__aux sr) vm) (happ (happ (happ (h4/canonical/interp__m sr) vm) c) l)) t)
% Assm [h4s_canonicals_icsu_u_auxu_u_defu_c1]: !vm t sr l a. happ (happ (happ (h4/canonical/ics__aux sr) vm) a) (happ (happ h4/canonical/Cons__varlist l) t) = happ (happ (h4/semi__ring/semi__ring__SRP sr) a) (happ (happ (happ (h4/canonical/ics__aux sr) vm) (happ (happ (h4/canonical/interp__vl sr) vm) l)) t)
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2]: !f0 f a0 a. h4/semi__ring/semi__ring__SRP (h4/semi__ring/semi__ring0 a a0 f f0) = f
% Assm [h4s_ringNorms_ru_u_interpu_u_csu_u_def]: !r. h4/ringNorm/r__interp__cs r = h4/canonical/interp__cs (h4/ring/semi__ring__of r)
% Assm [h4s_canonicals_interpu_u_csu_u_defu_c2]: !vm t sr l c. happ (happ (h4/canonical/interp__cs sr) vm) (happ (happ (happ h4/canonical/Cons__monom c) l) t) = happ (happ (happ (h4/canonical/ics__aux sr) vm) (happ (happ (happ (h4/canonical/interp__m sr) vm) c) l)) t
% Assm [h4s_canonicals_interpu_u_csu_u_defu_c1]: !vm t sr l. happ (happ (h4/canonical/interp__cs sr) vm) (happ (happ h4/canonical/Cons__varlist l) t) = happ (happ (happ (h4/canonical/ics__aux sr) vm) (happ (happ (h4/canonical/interp__vl sr) vm) l)) t
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c0]: !f0 f a0 a. h4/semi__ring/semi__ring__SR0 (h4/semi__ring/semi__ring0 a a0 f f0) = a
% Assm [h4s_ringNorms_varlistu_u_insertu_u_defu_c2]: !r l1. happ (happ (h4/ringNorm/r__varlist__insert r) l1) h4/canonical/Nil__monom = happ (happ h4/canonical/Cons__varlist l1) h4/canonical/Nil__monom
% Assm [h4s_ringNorms_varlistu_u_insertu_u_defu_c1]: !t2 r l2 l1. happ (happ (h4/ringNorm/r__varlist__insert r) l1) (happ (happ h4/canonical/Cons__varlist l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ h4/canonical/Cons__varlist l1) (happ (happ h4/canonical/Cons__varlist l2) t2)) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) (h4/ring/ring__R1 r)) (h4/ring/ring__R1 r))) l1) t2) (happ (happ h4/canonical/Cons__varlist l2) (happ (happ (h4/ringNorm/r__varlist__insert r) l1) t2))
% Assm [h4s_ringNorms_varlistu_u_insertu_u_defu_c0]: !t2 r l2 l1 c2. happ (happ (h4/ringNorm/r__varlist__insert r) l1) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2) = h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2) (happ (happ h4/canonical/Cons__varlist l1) (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2)) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/ring/ring__RP r) (h4/ring/ring__R1 r)) c2)) l1) t2) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ (happ (h4/ringNorm/r__varlist__insert r) l1) t2))
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalar2u_u_defu_c1]: !t r l0 l. happ (happ (h4/ringNorm/r__canonical__sum__scalar2 r) l0) (happ (happ h4/canonical/Cons__varlist l) t) = happ (happ (h4/ringNorm/r__varlist__insert r) (h4/prelim/list__merge h4/quote/index__lt l0 l)) (happ (happ (h4/ringNorm/r__canonical__sum__scalar2 r) l0) t)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalar2u_u_defu_c0]: !t r l0 l c. happ (happ (h4/ringNorm/r__canonical__sum__scalar2 r) l0) (happ (happ (happ h4/canonical/Cons__monom c) l) t) = happ (happ (happ (h4/ringNorm/r__monom__insert r) c) (h4/prelim/list__merge h4/quote/index__lt l0 l)) (happ (happ (h4/ringNorm/r__canonical__sum__scalar2 r) l0) t)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_scalar2u_u_defu_c2]: !r l0. happ (happ (h4/ringNorm/r__canonical__sum__scalar2 r) l0) h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_simplifyu_u_def]: h4/integerRing/int__r__canonical__sum__simplify = h4/ringNorm/r__canonical__sum__simplify (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_simplifyu_u_defu_c2]: !r. happ (h4/ringNorm/r__canonical__sum__simplify r) h4/canonical/Nil__monom = h4/canonical/Nil__monom
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_simplifyu_u_defu_c0]: !t r l c. ?v. (v <=> c = h4/ring/ring__R1 r) /\ (?v'. (v' <=> c = h4/ring/ring__R0 r) /\ happ (h4/ringNorm/r__canonical__sum__simplify r) (happ (happ (happ h4/canonical/Cons__monom c) l) t) = h4/bool/COND v' (happ (h4/ringNorm/r__canonical__sum__simplify r) t) (h4/bool/COND v (happ (happ h4/canonical/Cons__varlist l) (happ (h4/ringNorm/r__canonical__sum__simplify r) t)) (happ (happ (happ h4/canonical/Cons__monom c) l) (happ (h4/ringNorm/r__canonical__sum__simplify r) t))))
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_simplifyu_u_defu_c1]: !t r l. happ (h4/ringNorm/r__canonical__sum__simplify r) (happ (happ h4/canonical/Cons__varlist l) t) = happ (happ h4/canonical/Cons__varlist l) (happ (h4/ringNorm/r__canonical__sum__simplify r) t)
% Assm [h4s_rings_ringu_u_accessorsu_c0]: !f1 f0 f a0 a. h4/ring/ring__R0 (h4/ring/ring0 a a0 f f0 f1) = a
% Assm [h4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_produ_u_def]: h4/integerRing/int__r__canonical__sum__prod = h4/ringNorm/r__canonical__sum__prod (h4/ring/ring0 h4/integer/int__0 h4/integer/int__1 h4/integer/int__add h4/integer/int__mul h4/integer/int__neg)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c2]: !s2 r. happ (happ (h4/ringNorm/r__canonical__sum__prod r) h4/canonical/Nil__monom) s2 = h4/canonical/Nil__monom
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c1]: !t1 s2 r l1. happ (happ (h4/ringNorm/r__canonical__sum__prod r) (happ (happ h4/canonical/Cons__varlist l1) t1)) s2 = happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ (h4/ringNorm/r__canonical__sum__scalar2 r) l1) s2)) (happ (happ (h4/ringNorm/r__canonical__sum__prod r) t1) s2)
% Assm [h4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c0]: !t1 s2 r l1 c1. happ (happ (h4/ringNorm/r__canonical__sum__prod r) (happ (happ (happ h4/canonical/Cons__monom c1) l1) t1)) s2 = happ (happ (h4/ringNorm/r__canonical__sum__merge r) (happ (happ (happ (h4/ringNorm/r__canonical__sum__scalar3 r) c1) l1) s2)) (happ (happ (h4/ringNorm/r__canonical__sum__prod r) t1) s2)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Goal: !vm a. happ (happ (happ h4/integerRing/int__r__ics__aux vm) a) h4/canonical/Nil__monom = a
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_Q1255130,TV_Q1255126]: ![V_f, V_g]: (![V_x]: s(TV_Q1255126,happ(s(t_fun(TV_Q1255130,TV_Q1255126),V_f),s(TV_Q1255130,V_x))) = s(TV_Q1255126,happ(s(t_fun(TV_Q1255130,TV_Q1255126),V_g),s(TV_Q1255130,V_x))) => s(t_fun(TV_Q1255130,TV_Q1255126),V_f) = s(t_fun(TV_Q1255130,TV_Q1255126),V_g))).
fof(ah4s_integerRings_intu_u_ru_u_icsu_u_auxu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_icsu_u_aux) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
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_rings_ringu_u_accessorsu_c3, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_fun(TV_u_27a,TV_u_27a),V_f1))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0)).
fof(ah4s_integerRings_intu_u_ru_u_ivlu_u_auxu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_interpu_u_pu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_rings_ringu_u_accessorsu_c2, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_fun(TV_u_27a,TV_u_27a),V_f1))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f)).
fof(ah4s_rings_ringu_u_accessorsu_c1, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_fun(TV_u_27a,TV_u_27a),V_f1))))) = s(TV_u_27a,V_a0)).
fof(ah4s_rings_ringu_u_accessorsu_c4, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_fun(TV_u_27a,TV_u_27a),V_f1))))) = s(t_fun(TV_u_27a,TV_u_27a),V_f1)).
fof(ah4s_ringNorms_interpu_u_pu_u_defu_c4, axiom, ![TV_u_27a]: ![V_vm, V_r, V_p1]: s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_popp(s(t_h4s_ringNorms_polynom(TV_u_27a),V_p1))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_rings_ringu_u_rn(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p1)))))).
fof(ah4s_ringNorms_interpu_u_pu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_r, V_c]: s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pconst(s(TV_u_27a,V_c))))) = s(TV_u_27a,V_c)).
fof(ah4s_ringNorms_interpu_u_pu_u_defu_c1, axiom, ![TV_u_27a]: ![V_vm, V_r, V_i]: s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pvar(s(t_h4s_quotes_index,V_i))))) = s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_i),s(t_h4s_quotes_varmap(TV_u_27a),V_vm)))).
fof(ah4s_ringNorms_interpu_u_pu_u_defu_c3, axiom, ![TV_u_27a]: ![V_vm, V_r, V_p2, V_p1]: s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pmult(s(t_h4s_ringNorms_polynom(TV_u_27a),V_p1),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p2))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p1))))),s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p2)))))).
fof(ah4s_ringNorms_interpu_u_pu_u_defu_c2, axiom, ![TV_u_27a]: ![V_vm, V_r, V_p2, V_p1]: s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_pplus(s(t_h4s_ringNorms_polynom(TV_u_27a),V_p1),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p2))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p1))))),s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p2)))))).
fof(ah4s_ringNorms_ivlu_u_auxu_u_defu_c0, axiom, ![TV_u_27a]: ![V_x, V_vm, V_r]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))) = s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_x),s(t_h4s_quotes_varmap(TV_u_27a),V_vm)))).
fof(ah4s_ringNorms_ivlu_u_auxu_u_defu_c1, axiom, ![TV_u_27a]: ![V_xu_27, V_x, V_vm, V_tu_27, V_r]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_xu_27),s(t_h4s_lists_list(t_h4s_quotes_index),V_tu_27))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_x),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_quotes_index,V_xu_27))),s(t_h4s_lists_list(t_h4s_quotes_index),V_tu_27)))))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c1, axiom, ![V_vm, V_p]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_simplify),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p)))))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c43, axiom, ![V_vm, V_c]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_interpu_u_m),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_integers_int,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))) = s(t_h4s_integers_int,V_c)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c44, axiom, ![V_x, V_vm, V_t, V_c]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_interpu_u_m),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_integers_int,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_x),s(t_h4s_lists_list(t_h4s_quotes_index),V_t))))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_h4s_integers_int,V_c))),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_t)))))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c2, axiom, ![V_vm, V_c]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_pconst(s(t_h4s_integers_int,V_c))))) = s(t_h4s_integers_int,V_c)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c41, axiom, ![V_vm]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_vl),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))) = s(t_h4s_integers_int,h4s_integers_intu_u_1)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c4, axiom, ![V_vm, V_p2, V_p1]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_pplus(s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p1),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p2))))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p1))))),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p2)))))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c42, axiom, ![V_x, V_vm, V_t]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_vl),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_x),s(t_h4s_lists_list(t_h4s_quotes_index),V_t))))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_t)))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c6, axiom, ![V_vm, V_p1]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_popp(s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p1))))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p1)))))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c3, axiom, ![V_vm, V_i]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_pvar(s(t_h4s_quotes_index,V_i))))) = s(t_h4s_integers_int,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_i),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm)))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c39, axiom, ![V_x, V_vm]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))) = s(t_h4s_integers_int,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_x),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm)))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c5, axiom, ![V_vm, V_p2, V_p1]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),h4s_ringnorms_pmult(s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p1),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p2))))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p1))))),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_interpu_u_p),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_ringNorms_polynom(t_h4s_integers_int),V_p2)))))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c40, axiom, ![V_xu_27, V_x, V_vm, V_tu_27]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_xu_27),s(t_h4s_lists_list(t_h4s_quotes_index),V_tu_27))))) = s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_h4s_integers_int,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_x),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))))),s(t_h4s_integers_int,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_ivlu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_quotes_index,V_xu_27))),s(t_h4s_lists_list(t_h4s_quotes_index),V_tu_27)))))).
fof(ah4s_ringNorms_interpu_u_mu_u_defu_c1, axiom, ![TV_u_27a]: ![V_x, V_vm, V_t, V_r, V_c]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_interpu_u_m(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_x),s(t_h4s_lists_list(t_h4s_quotes_index),V_t))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_t)))))).
fof(ah4s_ringNorms_interpu_u_mu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_r, V_c]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_interpu_u_m(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))) = s(TV_u_27a,V_c)).
fof(ah4s_integerRings_intu_u_ru_u_interpu_u_mu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_interpu_u_m) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int))),h4s_ringnorms_ru_u_interpu_u_m(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ru_u_interpu_u_vlu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_vl) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_integers_int)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_ringNorms_interpu_u_vlu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_r]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))) = s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_ringNorms_interpu_u_vlu_u_defu_c1, axiom, ![TV_u_27a]: ![V_x, V_vm, V_t, V_r]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_x),s(t_h4s_lists_list(t_h4s_quotes_index),V_t))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_quotes_index,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_ivlu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_quotes_index,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_t)))).
fof(ah4s_integerRings_intu_u_ru_u_interpu_u_csu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_interpu_u_cs) = s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_ringNorms_polynomu_u_simplifyu_u_ok, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(TV_u_27a),V_r)))) => ![V_vm, V_p]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_polynomu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_interpu_u_p(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_p))))).
fof(ah4s_integerRings_intu_u_isu_u_ring, axiom, p(s(t_bool,h4s_rings_isu_u_ring(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg))))))).
fof(ah4s_integerRings_intu_u_polynomu_u_simplifyu_u_def, axiom, s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_polynomu_u_simplify) = s(t_fun(t_h4s_ringNorms_polynom(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_ringnorms_polynomu_u_simplify(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_canonicals_icsu_u_auxu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_sr, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_a))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(TV_u_27a,V_a)).
fof(ah4s_canonicals_interpu_u_csu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_sr]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_cs(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr)))).
fof(ah4s_ringNorms_interpu_u_csu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_r]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),V_r)))).
fof(ah4s_ringNorms_icsu_u_auxu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_r, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_a))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(TV_u_27a,V_a)).
fof(ah4s_integerRings_intu_u_ru_u_monomu_u_insertu_u_def, axiom, s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_monomu_u_insert) = s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_mergeu_u_def, axiom, s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_merge) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c20, axiom, ![V_l1, V_c1]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_monomu_u_insert),s(t_h4s_integers_int,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_canonicals_consu_u_monom),s(t_h4s_integers_int,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c32, axiom, ![V_l0, V_c0]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3),s(t_h4s_integers_int,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c26, axiom, ![V_c0]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar),s(t_h4s_integers_int,V_c0))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c16, axiom, ![V_v6, V_v5, V_v4]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_canonicals_consu_u_monom),s(t_h4s_integers_int,V_v4))),s(t_h4s_lists_list(t_h4s_quotes_index),V_v5))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),V_v6))))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_canonicals_consu_u_monom),s(t_h4s_integers_int,V_v4))),s(t_h4s_lists_list(t_h4s_quotes_index),V_v5))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),V_v6)))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c23, axiom, ![V_l1]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_varlistu_u_insert),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c29, axiom, ![V_l0]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar2),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c35, axiom, ![V_s2]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_prod),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),V_s2))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c38, axiom, s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_simplify),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom)).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c17, axiom, ![V_v8, V_v7]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_v7))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),V_v8))))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_v7))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),V_v8)))).
fof(ah4s_integerRings_intu_u_ringu_u_thmsu_c15, axiom, ![V_s1]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),V_s1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),V_s1)).
fof(ah4s_canonicals_monomu_u_insertu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_13]: (![V_l2u_27, V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_l1, V_t2u_27]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),V_uu_13),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2u_27))),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2u_27))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_combins_i(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2u_27))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2u_27))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2u_27))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2u_27))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2u_27))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_pairs_u_2c(s(TV_u_27a,V_c1),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2u_27))))))))))))))) => ![V_uu_12]: (![V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_l1, V_l2u_27]: s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),V_uu_12),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2u_27))) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),V_uu_13),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2u_27))),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))) => ![V_uu_11]: (![V_c2, V_l2, V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_l1, V_t2]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))))),V_uu_11),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_combins_i(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(TV_u_27a,V_c2))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_pairs_u_2c(s(TV_u_27a,V_c1),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))))))))))) => ![V_uu_10]: (![V_c2, V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_l1, V_l2]: s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))))),V_uu_10),s(TV_u_27a,V_c2))),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))))),V_uu_11),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))) => ![V_uu_9]: (![V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_l1, V_c2]: s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(TV_u_27a,V_c2))) = s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))))),V_uu_10),s(TV_u_27a,V_c2))),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))) => ![V_uu_8]: (![V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_l1, V_v5]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_v5))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_canonicalu_u_sumu_u_case(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_v5),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_combins_i(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))))),V_uu_12),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))))) => ![V_uu_7]: (![V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_l1]: s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))) => ![V_uu_6]: (![V_monomu_u_insertu_u_tupled, V_sr, V_c1, V_v3]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_v3))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_v3),s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))))) => ![V_uu_5]: (![V_monomu_u_insertu_u_tupled, V_sr, V_c1]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_c1))) => ![V_uu_4]: (![V_monomu_u_insertu_u_tupled, V_sr, V_v1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),V_v1))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),V_v1),s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))) => ![V_uu_3]: (![V_monomu_u_insertu_u_tupled, V_sr]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))) => ![V_uu_2]: (![V_monomu_u_insertu_u_tupled, V_a]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),V_a))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),V_a),s(t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))))) => ![V_uu_1]: (![V_monomu_u_insertu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_monomu_u_insertu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool)),V_R)))) & (![V_l2, V_c2, V_t2, V_l1, V_c1, V_sr]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_pairs_u_2c(s(TV_u_27a,V_c1),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))))),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_pairs_u_2c(s(TV_u_27a,V_c1),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))))))) & ![V_l2, V_t2, V_l1, V_c1, V_sr]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_pairs_u_2c(s(TV_u_27a,V_c1),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))))),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_pairs_u_2c(s(TV_u_27a,V_c1),s(t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_monomu_u_insertu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),V_uu_1)))))))))))))))))).
fof(ah4s_canonicals_canonicalu_u_sumu_u_distinctu_c1, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_a0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_a1))))).
fof(ah4s_rings_semiu_u_ringu_u_ofu_u_def, axiom, ![TV_u_27a]: ![V_r]: s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(TV_u_27a),V_r))) = s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ring0(s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_ringNorms_ru_u_interpu_u_vlu_u_def, axiom, ![TV_u_27a]: ![V_r]: s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_vl(s(t_h4s_rings_ring(TV_u_27a),V_r))) = s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_canonicals_interpu_u_vl(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_ringNorms_ru_u_interpu_u_mu_u_def, axiom, ![TV_u_27a]: ![V_r]: s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_ringnorms_ru_u_interpu_u_m(s(t_h4s_rings_ring(TV_u_27a),V_r))) = s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_canonicals_interpu_u_m(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_ringNorms_ru_u_icsu_u_auxu_u_def, axiom, ![TV_u_27a]: ![V_r]: s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_ringnorms_ru_u_icsu_u_aux(s(t_h4s_rings_ring(TV_u_27a),V_r))) = s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_integerRings_intu_u_ru_u_varlistu_u_insertu_u_def, axiom, s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_varlistu_u_insert) = s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3u_u_def, axiom, s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar3) = s(t_fun(t_h4s_integers_int,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c5, axiom, ![TV_u_27a]: ![V_v6, V_v5, V_v4, V_r]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_v4))),s(t_h4s_lists_list(t_h4s_quotes_index),V_v5))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_v6))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_v4))),s(t_h4s_lists_list(t_h4s_quotes_index),V_v5))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_v6)))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c4, axiom, ![TV_u_27a]: ![V_s1, V_r]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s1)).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_r, V_l2, V_l1, V_c2, V_c1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(TV_u_27a,V_c2))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_r, V_l2, V_l1, V_c1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_r, V_l2, V_l1, V_c2]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))),s(TV_u_27a,V_c2))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c3, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_r, V_l2, V_l1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_mergeu_u_defu_c6, axiom, ![TV_u_27a]: ![V_v8, V_v7, V_r]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_v7))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_v8))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_v7))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_v8)))).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalar2u_u_def, axiom, s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar2) = s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_scalaru_u_def, axiom, s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_scalar) = s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_c0]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c0, axiom, ![TV_u_27a]: ![V_t, V_r, V_l, V_c0, V_c]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(TV_u_27a,V_c))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalaru_u_defu_c1, axiom, ![TV_u_27a]: ![V_t, V_r, V_l, V_c0]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_ringNorms_monomu_u_insertu_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_l1, V_c1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_ringNorms_monomu_u_insertu_u_defu_c0, axiom, ![TV_u_27a]: ![V_t2, V_r, V_l2, V_l1, V_c2, V_c1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(TV_u_27a,V_c2))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_ringNorms_monomu_u_insertu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t2, V_r, V_l2, V_l1, V_c1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
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_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical2u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical2),s(t_h4s_lists_list(t_h4s_quotes_index),V_x))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_x0))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_lists_list(t_h4s_quotes_index),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_canonicals_u_20u_40indu_u_typecanonical4(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0))))))))).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
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_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => p(s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_canonicals_canonicalu_u_sumu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27canonicalu_u_sumu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0))) | (?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)),h4s_pairs_u_2c(s(TV_u_27a,V_a0),s(t_h4s_lists_list(t_h4s_quotes_index),V_a1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),t_bool),V_uu_27canonicalu_u_sumu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a2))))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_lists_list(t_h4s_quotes_index),V_a0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),t_bool),V_uu_27canonicalu_u_sumu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a1))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),t_bool),V_uu_27canonicalu_u_sumu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),t_bool),V_uu_27canonicalu_u_sumu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_canonicals_u_20u_40indu_u_typecanonical4(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),V_r)))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_bottom) => s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical0) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0))))))).
fof(ah4s_canonicals_Consu_u_varlist0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist) = s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical2)).
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_canonicals_Consu_u_monom0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_u_20u_40indu_u_typecanonical1)).
fof(ah4s_canonicals_Nilu_u_monom0, axiom, ![TV_u_27a]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical0)).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_bottom) => ![V_x, V_x0, V_x1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_u_20u_40indu_u_typecanonical1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_x0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_x1))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_lists_list(t_h4s_quotes_index),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_canonicals_u_20u_40indu_u_typecanonical4(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_x1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index)))),V_uu_0))))))))).
fof(ah4s_canonicals_canonicalu_u_sumu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_lists_list(t_h4s_quotes_index))),h4s_canonicals_u_20u_40indu_u_typecanonical4(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_a))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_a)).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
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_ringNorms_canonicalu_u_sumu_u_scalar3u_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_l0, V_c0]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalar3u_u_defu_c1, axiom, ![TV_u_27a]: ![V_t, V_r, V_l0, V_l, V_c0]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_prelims_listu_u_merge(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_bool)),h4s_quotes_indexu_u_lt),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalar3u_u_defu_c0, axiom, ![TV_u_27a]: ![V_t, V_r, V_l0, V_l, V_c0, V_c]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rm(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(TV_u_27a,V_c))))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_prelims_listu_u_merge(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_bool)),h4s_quotes_indexu_u_lt),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_canonicals_icsu_u_auxu_u_defu_c2, axiom, ![TV_u_27a]: ![V_vm, V_t, V_sr, V_l, V_c, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_a))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_a))),s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_canonicals_interpu_u_m(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_canonicals_icsu_u_auxu_u_defu_c1, axiom, ![TV_u_27a]: ![V_vm, V_t, V_sr, V_l, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_a))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,V_a))),s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_canonicals_interpu_u_vl(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c2, axiom, ![TV_u_27a]: ![V_f0, V_f, V_a0, V_a]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_semiu_u_rings_semiu_u_ringu_u_srp(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f)).
fof(ah4s_ringNorms_ru_u_interpu_u_csu_u_def, axiom, ![TV_u_27a]: ![V_r]: s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_cs(s(t_h4s_rings_ring(TV_u_27a),V_r))) = s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_cs(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_rings_semiu_u_ringu_u_of(s(t_h4s_rings_ring(TV_u_27a),V_r)))))).
fof(ah4s_canonicals_interpu_u_csu_u_defu_c2, axiom, ![TV_u_27a]: ![V_vm, V_t, V_sr, V_l, V_c]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_cs(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a))),h4s_canonicals_interpu_u_m(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))).
fof(ah4s_canonicals_interpu_u_csu_u_defu_c1, axiom, ![TV_u_27a]: ![V_vm, V_t, V_sr, V_l]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_cs(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a)),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27a))),h4s_canonicals_icsu_u_aux(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_quotes_index),TV_u_27a)),h4s_canonicals_interpu_u_vl(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c0, axiom, ![TV_u_27a]: ![V_f0, V_f, V_a0, V_a]: s(TV_u_27a,h4s_semiu_u_rings_semiu_u_ringu_u_sr0(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),h4s_semiu_u_rings_semiu_u_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0))))) = s(TV_u_27a,V_a)).
fof(ah4s_ringNorms_varlistu_u_insertu_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_l1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_ringNorms_varlistu_u_insertu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t2, V_r, V_l2, V_l1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_ringNorms_varlistu_u_insertu_u_defu_c0, axiom, ![TV_u_27a]: ![V_t2, V_r, V_l2, V_l1, V_c2]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_prelims_compare(s(t_h4s_prelims_ordering,h4s_prelims_listu_u_compare(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_h4s_prelims_ordering)),h4s_quotes_indexu_u_compare),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_rings_ringu_u_rp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r))))),s(TV_u_27a,V_c2))))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c2))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l2))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t2)))))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalar2u_u_defu_c1, axiom, ![TV_u_27a]: ![V_t, V_r, V_l0, V_l]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_varlistu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_prelims_listu_u_merge(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_bool)),h4s_quotes_indexu_u_lt),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalar2u_u_defu_c0, axiom, ![TV_u_27a]: ![V_t, V_r, V_l0, V_l, V_c]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_monomu_u_insert(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_prelims_listu_u_merge(s(t_fun(t_h4s_quotes_index,t_fun(t_h4s_quotes_index,t_bool)),h4s_quotes_indexu_u_lt),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_scalar2u_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_l0]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l0))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_simplifyu_u_def, axiom, s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_simplify) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_simplifyu_u_defu_c2, axiom, ![TV_u_27a]: ![V_r]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_simplifyu_u_defu_c0, axiom, ![TV_u_27a]: ![V_t, V_r, V_l, V_c]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_c) = s(TV_u_27a,h4s_rings_ringu_u_r1(s(t_h4s_rings_ring(TV_u_27a),V_r)))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(TV_u_27a,V_c) = s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),V_r)))) & s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))))))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_simplifyu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t, V_r, V_l]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t))))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_simplify(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t)))))).
fof(ah4s_rings_ringu_u_accessorsu_c0, axiom, ![TV_u_27a]: ![V_f1, V_f0, V_f, V_a0, V_a]: s(TV_u_27a,h4s_rings_ringu_u_r0(s(t_h4s_rings_ring(TV_u_27a),h4s_rings_ring0(s(TV_u_27a,V_a),s(TV_u_27a,V_a0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f0),s(t_fun(TV_u_27a,TV_u_27a),V_f1))))) = s(TV_u_27a,V_a)).
fof(ah4s_integerRings_intu_u_ru_u_canonicalu_u_sumu_u_produ_u_def, axiom, s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_canonicalu_u_sumu_u_prod) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(t_h4s_integers_int),h4s_rings_ring0(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_1),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_mul),s(t_fun(t_h4s_integers_int,t_h4s_integers_int),h4s_integers_intu_u_neg)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c2, axiom, ![TV_u_27a]: ![V_s2, V_r]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s2))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c1, axiom, ![TV_u_27a]: ![V_t1, V_s2, V_r, V_l1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s2))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar2(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s2)))))).
fof(ah4s_ringNorms_canonicalu_u_sumu_u_produ_u_defu_c0, axiom, ![TV_u_27a]: ![V_t1, V_s2, V_r, V_l1, V_c1]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_canonicals_consu_u_monom),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s2))) = s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_merge(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_scalar3(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(TV_u_27a,V_c1))),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s2))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a))),h4s_ringnorms_ru_u_canonicalu_u_sumu_u_prod(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_t1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_s2)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> 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(ch4s_integerRings_intu_u_ringu_u_thmsu_c45, conjecture, ![V_vm, V_a]: s(t_h4s_integers_int,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int)),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_integers_int),t_fun(t_h4s_integers_int,t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),t_h4s_integers_int))),h4s_integerrings_intu_u_ru_u_icsu_u_aux),s(t_h4s_quotes_varmap(t_h4s_integers_int),V_vm))),s(t_h4s_integers_int,V_a))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_integers_int),h4s_canonicals_nilu_u_monom))) = s(t_h4s_integers_int,V_a)).
