%   ORIGINAL: h4/numRing/num__ring__thms_c50
% 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/canonical/spolynom__normalize__def_c0: !sr i. h4/canonical/spolynom__normalize sr (h4/canonical/SPvar i) = h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL) h4/canonical/Nil__monom
% Assm: h4/numRing/num__spolynom__normalize__def: h4/numRing/num__spolynom__normalize = h4/canonical/spolynom__normalize (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm: h4/ringNorm/spolynom__normalize__def_c0: !r i. h4/ringNorm/r__spolynom__normalize r (h4/canonical/SPvar i) = h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL) h4/canonical/Nil__monom
% Assm: h4/ringNorm/polynom__normalize__def_c0: !r i. h4/ringNorm/polynom__normalize r (h4/ringNorm/Pvar i) = h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL) h4/canonical/Nil__monom
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/canonical/SPvar0: h4/canonical/SPvar = h4/canonical/_20_40ind__typecanonical5
% 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/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/canonical/spolynom__normalize__def_c1: !sr c. h4/canonical/spolynom__normalize sr (h4/canonical/SPconst c) = h4/canonical/Cons__monom c h4/list/NIL h4/canonical/Nil__monom
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/canonical/spolynom__normalize__def_c3: !sr r l. h4/canonical/spolynom__normalize sr (h4/canonical/SPmult l r) = h4/canonical/canonical__sum__prod sr (h4/canonical/spolynom__normalize sr l) (h4/canonical/spolynom__normalize sr r)
% Assm: h4/canonical/spolynom__normalize__def_c2: !sr r l. h4/canonical/spolynom__normalize sr (h4/canonical/SPplus l r) = h4/canonical/canonical__sum__merge sr (h4/canonical/spolynom__normalize sr l) (h4/canonical/spolynom__normalize sr r)
% Assm: h4/ringNorm/r__spolynom__normalize__def: !r. h4/ringNorm/r__spolynom__normalize r = h4/canonical/spolynom__normalize (h4/ring/semi__ring__of r)
% Assm: h4/ringNorm/r__canonical__sum__merge__def: !r. h4/ringNorm/r__canonical__sum__merge r = h4/canonical/canonical__sum__merge (h4/ring/semi__ring__of r)
% Assm: h4/ringNorm/r__canonical__sum__prod__def: !r. h4/ringNorm/r__canonical__sum__prod r = h4/canonical/canonical__sum__prod (h4/ring/semi__ring__of r)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% 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/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/canonical/SPconst0: h4/canonical/SPconst = h4/canonical/_20_40ind__typecanonical6
% Assm: h4/canonical/hidden____20__40ind____typecanonical5____def: h4/canonical/_20_40ind__typecanonical5 = (\a. h4/canonical/_20_40ind__typecanonical9 ((\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/canonical/spolynom__repfns_c0: !a. h4/canonical/_20_40ind__typecanonical9 (h4/canonical/_20_40ind__typecanonical10 a) = a
% Assm: h4/canonical/SPmult0: h4/canonical/SPmult = h4/canonical/_20_40ind__typecanonical8
% Assm: h4/canonical/hidden____20__40ind____typecanonical6____def: h4/canonical/_20_40ind__typecanonical6 = (\a. h4/canonical/_20_40ind__typecanonical9 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/canonical/SPplus0: h4/canonical/SPplus = h4/canonical/_20_40ind__typecanonical7
% Assm: h4/canonical/hidden____20__40ind____typecanonical8____def: h4/canonical/_20_40ind__typecanonical8 = (\a0 a1. h4/canonical/_20_40ind__typecanonical9 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/canonical/_20_40ind__typecanonical10 a0) (h4/canonical/_20_40ind__typecanonical10 a1)))
% Assm: h4/canonical/hidden____20__40ind____typecanonical7____def: h4/canonical/_20_40ind__typecanonical7 = (\a0 a1. h4/canonical/_20_40ind__typecanonical9 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/canonical/_20_40ind__typecanonical10 a0) (h4/canonical/_20_40ind__typecanonical10 a1)))
% Assm: h4/canonical/spolynom__repfns_c1: !r. (\a0_27. !_27spolynom_27. (!a0_270. (?a. a0_270 = (\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a) \/ (?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 h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27spolynom_27 a0 /\ _27spolynom_27 a1) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27spolynom_27 a0 /\ _27spolynom_27 a1) ==> _27spolynom_27 a0_270) ==> _27spolynom_27 a0_27) r <=> h4/canonical/_20_40ind__typecanonical10 (h4/canonical/_20_40ind__typecanonical9 r) = r
% Assm: h4/canonical/interp__sp__def_c1: !vm sr i. h4/canonical/interp__sp sr vm (h4/canonical/SPvar i) = h4/quote/varmap__find i vm
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/canonical/spolynom__case__def_c0: !f3 f2 f1 f a. h4/canonical/spolynom__CASE (h4/canonical/SPvar a) f f1 f2 f3 = f a
% Assm: h4/numRing/num__ring__thms_c3: !vm i. h4/numRing/num__interp__sp vm (h4/canonical/SPvar i) = h4/quote/varmap__find i vm
% Assm: h4/canonical/spolynom__size__def_c0: !f a. h4/canonical/spolynom__size f (h4/canonical/SPvar a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/quote/index__size a)
% Assm: h4/canonical/spolynom__distinct_c2: !a1 a0 a. ~(h4/canonical/SPvar a = h4/canonical/SPmult a0 a1)
% Assm: h4/canonical/spolynom__Axiom: !f3 f2 f1 f0. ?fn. (!a. fn (h4/canonical/SPvar a) = f0 a) /\ (!a. fn (h4/canonical/SPconst a) = f1 a) /\ (!a0 a1. fn (h4/canonical/SPplus a0 a1) = f2 a0 a1 (fn a0) (fn a1)) /\ (!a0 a1. fn (h4/canonical/SPmult a0 a1) = f3 a0 a1 (fn a0) (fn a1))
% Assm: h4/canonical/spolynom__nchotomy: !ss. (?i. ss = h4/canonical/SPvar i) \/ (?a. ss = h4/canonical/SPconst a) \/ (?s s0. ss = h4/canonical/SPplus s s0) \/ (?s s0. ss = h4/canonical/SPmult s s0)
% Assm: h4/canonical/spolynom__11_c0: !a_27 a. h4/canonical/SPvar a = h4/canonical/SPvar a_27 <=> a = a_27
% Assm: h4/canonical/spolynom__distinct_c1: !a1 a0 a. ~(h4/canonical/SPvar a = h4/canonical/SPplus a0 a1)
% Assm: h4/ringNorm/interp__sp__def_c1: !vm r i. h4/ringNorm/r__interp__sp r vm (h4/canonical/SPvar i) = h4/quote/varmap__find i vm
% Assm: h4/canonical/spolynom__case__cong: !f3_27 f3 f2_27 f2 f1_27 f1 f_27 f M_27 M. M = M_27 /\ (!a. M_27 = h4/canonical/SPvar a ==> f a = f_27 a) /\ (!a. M_27 = h4/canonical/SPconst a ==> f1 a = f1_27 a) /\ (!a0 a1. M_27 = h4/canonical/SPplus a0 a1 ==> f2 a0 a1 = f2_27 a0 a1) /\ (!a0 a1. M_27 = h4/canonical/SPmult a0 a1 ==> f3 a0 a1 = f3_27 a0 a1) ==> h4/canonical/spolynom__CASE M f f1 f2 f3 = h4/canonical/spolynom__CASE M_27 f_27 f1_27 f2_27 f3_27
% Assm: h4/canonical/spolynom__distinct_c0: !a_27 a. ~(h4/canonical/SPvar a = h4/canonical/SPconst a_27)
% Assm: h4/canonical/spolynom__induction: !P. (!i. P (h4/canonical/SPvar i)) /\ (!a. P (h4/canonical/SPconst a)) /\ (!s s0. P s /\ P s0 ==> P (h4/canonical/SPplus s s0)) /\ (!s s0. P s /\ P s0 ==> P (h4/canonical/SPmult s s0)) ==> (!s. P s)
% 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/canonical/datatype__spolynom: !spolynom. h4/bool/DATATYPE (spolynom h4/canonical/SPvar h4/canonical/SPconst h4/canonical/SPplus h4/canonical/SPmult)
% Assm: h4/canonical/interp__sp__def_c2: !vm sr p2 p1. h4/canonical/interp__sp sr vm (h4/canonical/SPplus p1 p2) = h4/semi__ring/semi__ring__SRP sr (h4/canonical/interp__sp sr vm p1) (h4/canonical/interp__sp sr vm p2)
% Assm: h4/canonical/interp__sp__def_c3: !vm sr p2 p1. h4/canonical/interp__sp sr vm (h4/canonical/SPmult p1 p2) = h4/semi__ring/semi__ring__SRM sr (h4/canonical/interp__sp sr vm p1) (h4/canonical/interp__sp sr vm p2)
% Assm: h4/canonical/interp__sp__def_c0: !vm sr c. h4/canonical/interp__sp sr vm (h4/canonical/SPconst c) = c
% Assm: h4/semi__ring/semi__ring__accessors_c3: !f0 f a0 a. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring0 a a0 f f0) = f0
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm2____def: h4/ringNorm/_20_40ind__typeringNorm2 = (\a0 a1. h4/ringNorm/_20_40ind__typeringNorm5 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/ringNorm/_20_40ind__typeringNorm6 a0) (h4/ringNorm/_20_40ind__typeringNorm6 a1)))
% Assm: h4/ringNorm/Popp0: h4/ringNorm/Popp = h4/ringNorm/_20_40ind__typeringNorm4
% Assm: h4/ringNorm/Pconst0: h4/ringNorm/Pconst = h4/ringNorm/_20_40ind__typeringNorm1
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm3____def: h4/ringNorm/_20_40ind__typeringNorm3 = (\a0 a1. h4/ringNorm/_20_40ind__typeringNorm5 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/ringNorm/_20_40ind__typeringNorm6 a0) (h4/ringNorm/_20_40ind__typeringNorm6 a1)))
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm4____def: h4/ringNorm/_20_40ind__typeringNorm4 = (\a. h4/ringNorm/_20_40ind__typeringNorm5 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/ringNorm/_20_40ind__typeringNorm6 a)))
% Assm: h4/ringNorm/Pmult0: h4/ringNorm/Pmult = h4/ringNorm/_20_40ind__typeringNorm3
% Assm: h4/ringNorm/Pplus0: h4/ringNorm/Pplus = h4/ringNorm/_20_40ind__typeringNorm2
% Assm: h4/ringNorm/Pvar0: h4/ringNorm/Pvar = h4/ringNorm/_20_40ind__typeringNorm0
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm1____def: h4/ringNorm/_20_40ind__typeringNorm1 = (\a. h4/ringNorm/_20_40ind__typeringNorm5 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/ringNorm/hidden____20__40ind____typeringNorm0____def: h4/ringNorm/_20_40ind__typeringNorm0 = (\a. h4/ringNorm/_20_40ind__typeringNorm5 ((\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/ringNorm/polynom__repfns_c1: !r. (\a0_27. !_27polynom_27. (!a0_270. (?a. a0_270 = (\a0. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 h4/bool/ARB) (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a0) (\n. h4/ind__type/BOTTOM)) a) \/ (?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 h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27polynom_27 a0 /\ _27polynom_27 a1) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27polynom_27 a0 /\ _27polynom_27 a1) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27polynom_27 a) ==> _27polynom_27 a0_270) ==> _27polynom_27 a0_27) r <=> h4/ringNorm/_20_40ind__typeringNorm6 (h4/ringNorm/_20_40ind__typeringNorm5 r) = r
% Assm: h4/ringNorm/polynom__repfns_c0: !a. h4/ringNorm/_20_40ind__typeringNorm5 (h4/ringNorm/_20_40ind__typeringNorm6 a) = a
% 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/numRing/num__interp__sp__def: h4/numRing/num__interp__sp = h4/canonical/interp__sp (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/canonical/varlist__insert__def_c2: !sr l1. h4/canonical/varlist__insert sr l1 h4/canonical/Nil__monom = h4/canonical/Cons__varlist l1 h4/canonical/Nil__monom
% Assm: h4/ringNorm/r__interp__sp__def: !r. h4/ringNorm/r__interp__sp r = h4/canonical/interp__sp (h4/ring/semi__ring__of r)
% Assm: h4/canonical/datatype__canonical__sum: !canonical__sum. h4/bool/DATATYPE (canonical__sum h4/canonical/Nil__monom h4/canonical/Cons__monom h4/canonical/Cons__varlist)
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/ringNorm/spolynom__normalize__def_c1: !r c. h4/ringNorm/r__spolynom__normalize r (h4/canonical/SPconst c) = h4/canonical/Cons__monom c h4/list/NIL h4/canonical/Nil__monom
% Assm: h4/canonical/varlist__insert__tupled__primitive__def: h4/canonical/varlist__insert__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!l2 c2 t2 l1 sr. R (h4/pair/_2C sr (h4/pair/_2C l1 t2)) (h4/pair/_2C sr (h4/pair/_2C l1 (h4/canonical/Cons__monom c2 l2 t2)))) /\ (!l2 t2 l1 sr. R (h4/pair/_2C sr (h4/pair/_2C l1 t2)) (h4/pair/_2C sr (h4/pair/_2C l1 (h4/canonical/Cons__varlist l2 t2)))))) (\varlist__insert__tupled a. h4/pair/pair__CASE a (\sr v1. h4/pair/pair__CASE v1 (\l1 v3. h4/canonical/canonical__sum__CASE v3 (h4/combin/I (h4/canonical/Cons__varlist 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__varlist l1 (h4/canonical/Cons__monom c2 l2 t2)) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr (h4/semi__ring/semi__ring__SR1 sr) c2) l1 t2) (h4/canonical/Cons__monom c2 l2 (varlist__insert__tupled (h4/pair/_2C sr (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__varlist l1 (h4/canonical/Cons__varlist l2_27 t2_27)) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr (h4/semi__ring/semi__ring__SR1 sr) (h4/semi__ring/semi__ring__SR1 sr)) l1 t2_27) (h4/canonical/Cons__varlist l2_27 (varlist__insert__tupled (h4/pair/_2C sr (h4/pair/_2C l1 t2_27)))))))))
% Assm: h4/numRing/num__ring__thms_c16: !v8 v7. h4/numRing/num__canonical__sum__merge h4/canonical/Nil__monom (h4/canonical/Cons__varlist v7 v8) = h4/canonical/Cons__varlist v7 v8
% Assm: h4/numRing/num__ring__thms_c22: !l1. h4/numRing/num__varlist__insert l1 h4/canonical/Nil__monom = h4/canonical/Cons__varlist l1 h4/canonical/Nil__monom
% 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/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/semi__ring/semi__ring__accessors_c1: !f0 f a0 a. h4/semi__ring/semi__ring__SR1 (h4/semi__ring/semi__ring0 a a0 f f0) = a0
% Assm: h4/canonical/varlist__insert__def_c1: !t2 sr l2 l1. h4/canonical/varlist__insert sr 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/semi__ring/semi__ring__SRP sr (h4/semi__ring/semi__ring__SR1 sr) (h4/semi__ring/semi__ring__SR1 sr)) l1 t2) (h4/canonical/Cons__varlist l2 (h4/canonical/varlist__insert sr l1 t2))
% Assm: h4/canonical/varlist__insert__def_c0: !t2 sr l2 l1 c2. h4/canonical/varlist__insert sr 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/semi__ring/semi__ring__SRP sr (h4/semi__ring/semi__ring__SR1 sr) c2) l1 t2) (h4/canonical/Cons__monom c2 l2 (h4/canonical/varlist__insert sr l1 t2))
% Assm: h4/canonical/spolynom__case__def_c3: !f3 f2 f1 f a1 a0. h4/canonical/spolynom__CASE (h4/canonical/SPmult a0 a1) f f1 f2 f3 = f3 a0 a1
% Assm: h4/canonical/spolynom__case__def_c1: !f3 f2 f1 f a. h4/canonical/spolynom__CASE (h4/canonical/SPconst a) f f1 f2 f3 = f1 a
% Assm: h4/canonical/spolynom__case__def_c2: !f3 f2 f1 f a1 a0. h4/canonical/spolynom__CASE (h4/canonical/SPplus a0 a1) f f1 f2 f3 = f2 a0 a1
% Assm: h4/numRing/num__varlist__insert__def: h4/numRing/num__varlist__insert = h4/canonical/varlist__insert (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm: h4/ringNorm/r__varlist__insert__def: !r. h4/ringNorm/r__varlist__insert r = h4/canonical/varlist__insert (h4/ring/semi__ring__of r)
% Assm: h4/canonical/canonical__sum__merge__def_c6: !v8 v7 sr. h4/canonical/canonical__sum__merge sr h4/canonical/Nil__monom (h4/canonical/Cons__varlist v7 v8) = h4/canonical/Cons__varlist v7 v8
% Assm: h4/canonical/canonical__sum__merge__def_c5: !v6 v5 v4 sr. h4/canonical/canonical__sum__merge sr h4/canonical/Nil__monom (h4/canonical/Cons__monom v4 v5 v6) = h4/canonical/Cons__monom v4 v5 v6
% Assm: h4/canonical/canonical__sum__merge__def_c2: !t2 t1 sr l2 l1 c2. h4/canonical/canonical__sum__merge sr (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/canonical/canonical__sum__merge sr t1 (h4/canonical/Cons__monom c2 l2 t2))) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr (h4/semi__ring/semi__ring__SR1 sr) c2) l1 (h4/canonical/canonical__sum__merge sr t1 t2)) (h4/canonical/Cons__monom c2 l2 (h4/canonical/canonical__sum__merge sr (h4/canonical/Cons__varlist l1 t1) t2))
% Assm: h4/canonical/canonical__sum__merge__def_c3: !t2 t1 sr l2 l1. h4/canonical/canonical__sum__merge sr (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/canonical/canonical__sum__merge sr t1 (h4/canonical/Cons__varlist l2 t2))) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr (h4/semi__ring/semi__ring__SR1 sr) (h4/semi__ring/semi__ring__SR1 sr)) l1 (h4/canonical/canonical__sum__merge sr t1 t2)) (h4/canonical/Cons__varlist l2 (h4/canonical/canonical__sum__merge sr (h4/canonical/Cons__varlist l1 t1) t2))
% Assm: h4/canonical/canonical__sum__merge__def_c1: !t2 t1 sr l2 l1 c1. h4/canonical/canonical__sum__merge sr (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/canonical/canonical__sum__merge sr t1 (h4/canonical/Cons__varlist l2 t2))) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr c1 (h4/semi__ring/semi__ring__SR1 sr)) l1 (h4/canonical/canonical__sum__merge sr t1 t2)) (h4/canonical/Cons__varlist l2 (h4/canonical/canonical__sum__merge sr (h4/canonical/Cons__monom c1 l1 t1) t2))
% Assm: h4/canonical/canonical__sum__merge__def_c4: !sr s1. h4/canonical/canonical__sum__merge sr s1 h4/canonical/Nil__monom = s1
% Assm: h4/canonical/canonical__sum__merge__def_c0: !t2 t1 sr l2 l1 c2 c1. h4/canonical/canonical__sum__merge sr (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/canonical/canonical__sum__merge sr t1 (h4/canonical/Cons__monom c2 l2 t2))) (h4/canonical/Cons__monom (h4/semi__ring/semi__ring__SRP sr c1 c2) l1 (h4/canonical/canonical__sum__merge sr t1 t2)) (h4/canonical/Cons__monom c2 l2 (h4/canonical/canonical__sum__merge sr (h4/canonical/Cons__monom c1 l1 t1) t2))
% Assm: h4/numRing/num__canonical__sum__merge__def: h4/numRing/num__canonical__sum__merge = h4/canonical/canonical__sum__merge (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/canonical/varlist__insert__curried__def: !x2 x1 x. h4/canonical/varlist__insert x x1 x2 = h4/canonical/varlist__insert__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/canonical/canonical__sum__size__def_c2: !f a1 a0. h4/canonical/canonical__sum__size f (h4/canonical/Cons__varlist a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/list/list__size h4/quote/index__size a0) (h4/canonical/canonical__sum__size f a1))
% Assm: h4/canonical/canonical__sum__case__def_c0: !v f1 f. h4/canonical/canonical__sum__CASE h4/canonical/Nil__monom v f f1 = v
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/canonical/canonical__sum__case__def_c1: !v f1 f a2 a1 a0. h4/canonical/canonical__sum__CASE (h4/canonical/Cons__monom a0 a1 a2) v f f1 = f a0 a1 a2
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/canonical/canonical__sum__case__def_c2: !v f1 f a1 a0. h4/canonical/canonical__sum__CASE (h4/canonical/Cons__varlist a0 a1) v f f1 = f1 a0 a1
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Goal: !i. h4/numRing/num__spolynom__normalize (h4/canonical/SPvar i) = h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL) h4/canonical/Nil__monom
%   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_canonicals_spolynomu_u_normalizeu_u_defu_c0]: !sr i. happ (h4/canonical/spolynom__normalize sr) (happ h4/canonical/SPvar i) = happ (happ h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL)) h4/canonical/Nil__monom
% Assm [h4s_numRings_numu_u_spolynomu_u_normalizeu_u_def]: h4/numRing/num__spolynom__normalize = h4/canonical/spolynom__normalize (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm [h4s_ringNorms_spolynomu_u_normalizeu_u_defu_c0]: !r i. happ (h4/ringNorm/r__spolynom__normalize r) (happ h4/canonical/SPvar i) = happ (happ h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL)) h4/canonical/Nil__monom
% Assm [h4s_ringNorms_polynomu_u_normalizeu_u_defu_c0]: !r i. h4/ringNorm/polynom__normalize r (happ h4/ringNorm/Pvar i) = happ (happ h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL)) h4/canonical/Nil__monom
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_canonicals_SPvar0]: h4/canonical/SPvar = h4/canonical/_20_40ind__typecanonical5
% 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_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_canonicals_spolynomu_u_normalizeu_u_defu_c1]: !sr c. happ (h4/canonical/spolynom__normalize sr) (happ h4/canonical/SPconst c) = happ (happ (happ h4/canonical/Cons__monom c) h4/list/NIL) h4/canonical/Nil__monom
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_canonicals_spolynomu_u_normalizeu_u_defu_c3]: !sr r l. happ (h4/canonical/spolynom__normalize sr) (happ (happ h4/canonical/SPmult l) r) = happ (happ (h4/canonical/canonical__sum__prod sr) (happ (h4/canonical/spolynom__normalize sr) l)) (happ (h4/canonical/spolynom__normalize sr) r)
% Assm [h4s_canonicals_spolynomu_u_normalizeu_u_defu_c2]: !sr r l. happ (h4/canonical/spolynom__normalize sr) (happ (happ h4/canonical/SPplus l) r) = happ (happ (h4/canonical/canonical__sum__merge sr) (happ (h4/canonical/spolynom__normalize sr) l)) (happ (h4/canonical/spolynom__normalize sr) r)
% Assm [h4s_ringNorms_ru_u_spolynomu_u_normalizeu_u_def]: !r. h4/ringNorm/r__spolynom__normalize r = h4/canonical/spolynom__normalize (h4/ring/semi__ring__of r)
% Assm [h4s_ringNorms_ru_u_canonicalu_u_sumu_u_mergeu_u_def]: !r. h4/ringNorm/r__canonical__sum__merge r = h4/canonical/canonical__sum__merge (h4/ring/semi__ring__of r)
% Assm [h4s_ringNorms_ru_u_canonicalu_u_sumu_u_produ_u_def]: !r. h4/ringNorm/r__canonical__sum__prod r = h4/canonical/canonical__sum__prod (h4/ring/semi__ring__of r)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% 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_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = 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_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_canonicals_SPconst0]: h4/canonical/SPconst = h4/canonical/_20_40ind__typecanonical6
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/canonical/_20_40ind__typecanonical5 x = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C x h4/bool/ARB) _0))
% Assm [h4s_canonicals_spolynomu_u_repfnsu_c0]: !a. h4/canonical/_20_40ind__typecanonical9 (h4/canonical/_20_40ind__typecanonical10 a) = a
% Assm [h4s_canonicals_SPmult0]: h4/canonical/SPmult = h4/canonical/_20_40ind__typecanonical8
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/canonical/_20_40ind__typecanonical6 x = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB x) _0))
% Assm [h4s_canonicals_SPplus0]: h4/canonical/SPplus = h4/canonical/_20_40ind__typecanonical7
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical8u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/canonical/_20_40ind__typecanonical8 x) x' = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x') _0))))
% Assm [h4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical7u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/canonical/_20_40ind__typecanonical7 x) x' = h4/canonical/_20_40ind__typecanonical9 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x) (h4/ind__type/FCONS (h4/canonical/_20_40ind__typecanonical10 x') _0))))
% Assm [h4s_canonicals_spolynomu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27spolynom_27. (!a0_270. (?a. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a h4/bool/ARB) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a) _0) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27spolynom_27 a0 /\ happ _27spolynom_27 a1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27spolynom_27 a0 /\ happ _27spolynom_27 a1) ==> happ _27spolynom_27 a0_270) ==> happ _27spolynom_27 r) <=> h4/canonical/_20_40ind__typecanonical10 (h4/canonical/_20_40ind__typecanonical9 r) = r)
% Assm [h4s_canonicals_interpu_u_spu_u_defu_c1]: !vm sr i. happ (happ (h4/canonical/interp__sp sr) vm) (happ h4/canonical/SPvar i) = h4/quote/varmap__find i vm
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_canonicals_spolynomu_u_caseu_u_defu_c0]: !f3 f2 f1 f a. h4/canonical/spolynom__CASE (happ h4/canonical/SPvar a) f f1 f2 f3 = happ f a
% Assm [h4s_numRings_numu_u_ringu_u_thmsu_c3]: !vm i. happ (happ h4/numRing/num__interp__sp vm) (happ h4/canonical/SPvar i) = h4/quote/varmap__find i vm
% Assm [h4s_canonicals_spolynomu_u_sizeu_u_defu_c0]: !f a. h4/canonical/spolynom__size f (happ h4/canonical/SPvar a) = happ (happ h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (happ h4/quote/index__size a)
% Assm [h4s_canonicals_spolynomu_u_distinctu_c2]: !a1 a0 a. ~(happ h4/canonical/SPvar a = happ (happ h4/canonical/SPmult a0) a1)
% Assm [h4s_canonicals_spolynomu_u_Axiom]: !f3 f2 f1 f0. ?fn. (!a. happ fn (happ h4/canonical/SPvar a) = happ f0 a) /\ (!a. happ fn (happ h4/canonical/SPconst a) = happ f1 a) /\ (!a0 a1. happ fn (happ (happ h4/canonical/SPplus a0) a1) = happ (happ (happ (happ f2 a0) a1) (happ fn a0)) (happ fn a1)) /\ (!a0 a1. happ fn (happ (happ h4/canonical/SPmult a0) a1) = happ (happ (happ (happ f3 a0) a1) (happ fn a0)) (happ fn a1))
% Assm [h4s_canonicals_spolynomu_u_nchotomy]: !ss. (?i. ss = happ h4/canonical/SPvar i) \/ (?a. ss = happ h4/canonical/SPconst a) \/ (?s s0. ss = happ (happ h4/canonical/SPplus s) s0) \/ (?s s0. ss = happ (happ h4/canonical/SPmult s) s0)
% Assm [h4s_canonicals_spolynomu_u_11u_c0]: !a_27 a. happ h4/canonical/SPvar a = happ h4/canonical/SPvar a_27 <=> a = a_27
% Assm [h4s_canonicals_spolynomu_u_distinctu_c1]: !a1 a0 a. ~(happ h4/canonical/SPvar a = happ (happ h4/canonical/SPplus a0) a1)
% Assm [h4s_ringNorms_interpu_u_spu_u_defu_c1]: !vm r i. happ (happ (h4/ringNorm/r__interp__sp r) vm) (happ h4/canonical/SPvar i) = h4/quote/varmap__find i vm
% Assm [h4s_canonicals_spolynomu_u_caseu_u_cong]: !f3_27 f3 f2_27 f2 f1_27 f1 f_27 f M_27 M. M = M_27 /\ (!a. M_27 = happ h4/canonical/SPvar a ==> happ f a = happ f_27 a) /\ (!a. M_27 = happ h4/canonical/SPconst a ==> happ f1 a = happ f1_27 a) /\ (!a0 a1. M_27 = happ (happ h4/canonical/SPplus a0) a1 ==> happ (happ f2 a0) a1 = happ (happ f2_27 a0) a1) /\ (!a0 a1. M_27 = happ (happ h4/canonical/SPmult a0) a1 ==> happ (happ f3 a0) a1 = happ (happ f3_27 a0) a1) ==> h4/canonical/spolynom__CASE M f f1 f2 f3 = h4/canonical/spolynom__CASE M_27 f_27 f1_27 f2_27 f3_27
% Assm [h4s_canonicals_spolynomu_u_distinctu_c0]: !a_27 a. ~(happ h4/canonical/SPvar a = happ h4/canonical/SPconst a_27)
% Assm [h4s_canonicals_spolynomu_u_induction]: !P. (!i. happ P (happ h4/canonical/SPvar i)) /\ (!a. happ P (happ h4/canonical/SPconst a)) /\ (!s s0. happ P s /\ happ P s0 ==> happ P (happ (happ h4/canonical/SPplus s) s0)) /\ (!s s0. happ P s /\ happ P s0 ==> happ P (happ (happ h4/canonical/SPmult s) s0)) ==> (!s. happ P s)
% 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_canonicals_datatypeu_u_spolynom]: !spolynom. h4/bool/DATATYPE (happ (happ (happ (happ spolynom h4/canonical/SPvar) h4/canonical/SPconst) h4/canonical/SPplus) h4/canonical/SPmult)
% Assm [h4s_canonicals_interpu_u_spu_u_defu_c2]: !vm sr p2 p1. happ (happ (h4/canonical/interp__sp sr) vm) (happ (happ h4/canonical/SPplus p1) p2) = happ (happ (h4/semi__ring/semi__ring__SRP sr) (happ (happ (h4/canonical/interp__sp sr) vm) p1)) (happ (happ (h4/canonical/interp__sp sr) vm) p2)
% Assm [h4s_canonicals_interpu_u_spu_u_defu_c3]: !vm sr p2 p1. happ (happ (h4/canonical/interp__sp sr) vm) (happ (happ h4/canonical/SPmult p1) p2) = happ (happ (h4/semi__ring/semi__ring__SRM sr) (happ (happ (h4/canonical/interp__sp sr) vm) p1)) (happ (happ (h4/canonical/interp__sp sr) vm) p2)
% Assm [h4s_canonicals_interpu_u_spu_u_defu_c0]: !vm sr c. happ (happ (h4/canonical/interp__sp sr) vm) (happ h4/canonical/SPconst c) = c
% Assm [h4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c3]: !f0 f a0 a. h4/semi__ring/semi__ring__SRM (h4/semi__ring/semi__ring0 a a0 f f0) = f0
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/ringNorm/_20_40ind__typeringNorm2 x) x' = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x') _0))))
% Assm [h4s_ringNorms_Popp0]: h4/ringNorm/Popp = h4/ringNorm/_20_40ind__typeringNorm4
% Assm [h4s_ringNorms_Pconst0]: h4/ringNorm/Pconst = h4/ringNorm/_20_40ind__typeringNorm1
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm3u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/ringNorm/_20_40ind__typeringNorm3 x) x' = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x') _0))))
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/ringNorm/_20_40ind__typeringNorm4 x = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/ringNorm/_20_40ind__typeringNorm6 x) _0)))
% Assm [h4s_ringNorms_Pmult0]: h4/ringNorm/Pmult = h4/ringNorm/_20_40ind__typeringNorm3
% Assm [h4s_ringNorms_Pplus0]: h4/ringNorm/Pplus = h4/ringNorm/_20_40ind__typeringNorm2
% Assm [h4s_ringNorms_Pvar0]: h4/ringNorm/Pvar = h4/ringNorm/_20_40ind__typeringNorm0
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/ringNorm/_20_40ind__typeringNorm1 x = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB x) _0))
% Assm [h4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/ringNorm/_20_40ind__typeringNorm0 x = h4/ringNorm/_20_40ind__typeringNorm5 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C x h4/bool/ARB) _0))
% Assm [h4s_ringNorms_polynomu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27polynom_27. (!a0_270. (?a. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a h4/bool/ARB) _0) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB a) _0) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27polynom_27 a0 /\ happ _27polynom_27 a1) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27polynom_27 a0 /\ happ _27polynom_27 a1) \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0)))) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a _0) /\ happ _27polynom_27 a) ==> happ _27polynom_27 a0_270) ==> happ _27polynom_27 r) <=> h4/ringNorm/_20_40ind__typeringNorm6 (h4/ringNorm/_20_40ind__typeringNorm5 r) = r)
% Assm [h4s_ringNorms_polynomu_u_repfnsu_c0]: !a. h4/ringNorm/_20_40ind__typeringNorm5 (h4/ringNorm/_20_40ind__typeringNorm6 a) = a
% 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_numRings_numu_u_interpu_u_spu_u_def]: h4/numRing/num__interp__sp = h4/canonical/interp__sp (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_canonicals_varlistu_u_insertu_u_defu_c2]: !sr l1. happ (happ (h4/canonical/varlist__insert sr) l1) h4/canonical/Nil__monom = happ (happ h4/canonical/Cons__varlist l1) h4/canonical/Nil__monom
% Assm [h4s_ringNorms_ru_u_interpu_u_spu_u_def]: !r. h4/ringNorm/r__interp__sp r = h4/canonical/interp__sp (h4/ring/semi__ring__of r)
% Assm [h4s_canonicals_datatypeu_u_canonicalu_u_sum]: !canonical__sum. h4/bool/DATATYPE (happ (happ (happ canonical__sum h4/canonical/Nil__monom) h4/canonical/Cons__monom) h4/canonical/Cons__varlist)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_ringNorms_spolynomu_u_normalizeu_u_defu_c1]: !r c. happ (h4/ringNorm/r__spolynom__normalize r) (happ h4/canonical/SPconst c) = happ (happ (happ h4/canonical/Cons__monom c) h4/list/NIL) h4/canonical/Nil__monom
% Assm [h4s_canonicals_varlistu_u_insertu_u_tupledu_u_primitiveu_u_def]: !_11. (!l2_27 varlist__insert__tupled sr l1 t2_27. happ (happ (happ (happ (happ _11 l2_27) varlist__insert__tupled) sr) l1) t2_27 = h4/combin/I (h4/prelim/compare (h4/prelim/list__compare h4/quote/index__compare l1 l2_27) (happ (happ h4/canonical/Cons__varlist 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) (h4/semi__ring/semi__ring__SR1 sr)) (h4/semi__ring/semi__ring__SR1 sr))) l1) t2_27) (happ (happ h4/canonical/Cons__varlist l2_27) (happ varlist__insert__tupled (h4/pair/_2C sr (h4/pair/_2C l1 t2_27)))))) ==> (!_10. (!varlist__insert__tupled sr l1 l2_27. happ (happ (happ (happ _10 varlist__insert__tupled) sr) l1) l2_27 = happ (happ (happ (happ _11 l2_27) varlist__insert__tupled) sr) l1) ==> (!_9. (!c2 l2 varlist__insert__tupled sr l1 t2. happ (happ (happ (happ (happ (happ _9 c2) l2) varlist__insert__tupled) sr) l1) t2 = h4/combin/I (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/semi__ring/semi__ring__SRP sr) (h4/semi__ring/semi__ring__SR1 sr)) c2)) l1) t2) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ varlist__insert__tupled (h4/pair/_2C sr (h4/pair/_2C l1 t2)))))) ==> (!_8. (!c2 varlist__insert__tupled sr l1 l2. happ (happ (happ (happ (happ _8 c2) varlist__insert__tupled) sr) l1) l2 = happ (happ (happ (happ (happ _9 c2) l2) varlist__insert__tupled) sr) l1) ==> (!_7. (!varlist__insert__tupled sr l1 c2. happ (happ (happ (happ _7 varlist__insert__tupled) sr) l1) c2 = happ (happ (happ (happ _8 c2) varlist__insert__tupled) sr) l1) ==> (!_6. (!varlist__insert__tupled sr l1 v3. happ (happ (happ (happ _6 varlist__insert__tupled) sr) l1) v3 = h4/canonical/canonical__sum__CASE v3 (h4/combin/I (happ (happ h4/canonical/Cons__varlist l1) h4/canonical/Nil__monom)) (happ (happ (happ _7 varlist__insert__tupled) sr) l1) (happ (happ (happ _10 varlist__insert__tupled) sr) l1)) ==> (!_5. (!varlist__insert__tupled sr l1. happ (happ (happ _5 varlist__insert__tupled) sr) l1 = happ (happ (happ _6 varlist__insert__tupled) sr) l1) ==> (!_4. (!varlist__insert__tupled sr v1. happ (happ (happ _4 varlist__insert__tupled) sr) v1 = h4/pair/pair__CASE v1 (happ (happ _5 varlist__insert__tupled) sr)) ==> (!_3. (!varlist__insert__tupled sr. happ (happ _3 varlist__insert__tupled) sr = happ (happ _4 varlist__insert__tupled) sr) ==> (!_2. (!varlist__insert__tupled a. happ (happ _2 varlist__insert__tupled) a = h4/pair/pair__CASE a (happ _3 varlist__insert__tupled)) ==> (!_1. (!varlist__insert__tupled. happ _1 varlist__insert__tupled = happ _2 varlist__insert__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!l2 c2 t2 l1 sr. happ (happ R (h4/pair/_2C sr (h4/pair/_2C l1 t2))) (h4/pair/_2C sr (h4/pair/_2C l1 (happ (happ (happ h4/canonical/Cons__monom c2) l2) t2)))) /\ (!l2 t2 l1 sr. happ (happ R (h4/pair/_2C sr (h4/pair/_2C l1 t2))) (h4/pair/_2C sr (h4/pair/_2C l1 (happ (happ h4/canonical/Cons__varlist l2) t2))))) ==> h4/canonical/varlist__insert__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))))
% Assm [h4s_numRings_numu_u_ringu_u_thmsu_c16]: !v8 v7. happ (happ h4/numRing/num__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_numRings_numu_u_ringu_u_thmsu_c22]: !l1. happ (happ h4/numRing/num__varlist__insert l1) h4/canonical/Nil__monom = happ (happ h4/canonical/Cons__varlist l1) h4/canonical/Nil__monom
% 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_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_semiu_u_rings_semiu_u_ringu_u_accessorsu_c1]: !f0 f a0 a. h4/semi__ring/semi__ring__SR1 (h4/semi__ring/semi__ring0 a a0 f f0) = a0
% Assm [h4s_canonicals_varlistu_u_insertu_u_defu_c1]: !t2 sr l2 l1. happ (happ (h4/canonical/varlist__insert sr) 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/semi__ring/semi__ring__SRP sr) (h4/semi__ring/semi__ring__SR1 sr)) (h4/semi__ring/semi__ring__SR1 sr))) l1) t2) (happ (happ h4/canonical/Cons__varlist l2) (happ (happ (h4/canonical/varlist__insert sr) l1) t2))
% Assm [h4s_canonicals_varlistu_u_insertu_u_defu_c0]: !t2 sr l2 l1 c2. happ (happ (h4/canonical/varlist__insert sr) 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/semi__ring/semi__ring__SRP sr) (h4/semi__ring/semi__ring__SR1 sr)) c2)) l1) t2) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ (happ (h4/canonical/varlist__insert sr) l1) t2))
% Assm [h4s_canonicals_spolynomu_u_caseu_u_defu_c3]: !f3 f2 f1 f a1 a0. h4/canonical/spolynom__CASE (happ (happ h4/canonical/SPmult a0) a1) f f1 f2 f3 = happ (happ f3 a0) a1
% Assm [h4s_canonicals_spolynomu_u_caseu_u_defu_c1]: !f3 f2 f1 f a. h4/canonical/spolynom__CASE (happ h4/canonical/SPconst a) f f1 f2 f3 = happ f1 a
% Assm [h4s_canonicals_spolynomu_u_caseu_u_defu_c2]: !f3 f2 f1 f a1 a0. h4/canonical/spolynom__CASE (happ (happ h4/canonical/SPplus a0) a1) f f1 f2 f3 = happ (happ f2 a0) a1
% Assm [h4s_numRings_numu_u_varlistu_u_insertu_u_def]: h4/numRing/num__varlist__insert = h4/canonical/varlist__insert (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm [h4s_ringNorms_ru_u_varlistu_u_insertu_u_def]: !r. h4/ringNorm/r__varlist__insert r = h4/canonical/varlist__insert (h4/ring/semi__ring__of r)
% Assm [h4s_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c6]: !v8 v7 sr. happ (happ (h4/canonical/canonical__sum__merge sr) h4/canonical/Nil__monom) (happ (happ h4/canonical/Cons__varlist v7) v8) = happ (happ h4/canonical/Cons__varlist v7) v8
% Assm [h4s_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c5]: !v6 v5 v4 sr. happ (happ (h4/canonical/canonical__sum__merge sr) 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_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c2]: !t2 t1 sr l2 l1 c2. happ (happ (h4/canonical/canonical__sum__merge sr) (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/canonical/canonical__sum__merge sr) t1) (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) (h4/semi__ring/semi__ring__SR1 sr)) c2)) l1) (happ (happ (h4/canonical/canonical__sum__merge sr) t1) t2)) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ (happ (h4/canonical/canonical__sum__merge sr) (happ (happ h4/canonical/Cons__varlist l1) t1)) t2))
% Assm [h4s_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c3]: !t2 t1 sr l2 l1. happ (happ (h4/canonical/canonical__sum__merge sr) (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/canonical/canonical__sum__merge sr) t1) (happ (happ h4/canonical/Cons__varlist l2) t2))) (happ (happ (happ h4/canonical/Cons__monom (happ (happ (h4/semi__ring/semi__ring__SRP sr) (h4/semi__ring/semi__ring__SR1 sr)) (h4/semi__ring/semi__ring__SR1 sr))) l1) (happ (happ (h4/canonical/canonical__sum__merge sr) t1) t2)) (happ (happ h4/canonical/Cons__varlist l2) (happ (happ (h4/canonical/canonical__sum__merge sr) (happ (happ h4/canonical/Cons__varlist l1) t1)) t2))
% Assm [h4s_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c1]: !t2 t1 sr l2 l1 c1. happ (happ (h4/canonical/canonical__sum__merge sr) (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/canonical/canonical__sum__merge sr) t1) (happ (happ h4/canonical/Cons__varlist l2) t2))) (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) (happ (happ (h4/canonical/canonical__sum__merge sr) t1) t2)) (happ (happ h4/canonical/Cons__varlist l2) (happ (happ (h4/canonical/canonical__sum__merge sr) (happ (happ (happ h4/canonical/Cons__monom c1) l1) t1)) t2))
% Assm [h4s_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c4]: !sr s1. happ (happ (h4/canonical/canonical__sum__merge sr) s1) h4/canonical/Nil__monom = s1
% Assm [h4s_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c0]: !t2 t1 sr l2 l1 c2 c1. happ (happ (h4/canonical/canonical__sum__merge sr) (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/canonical/canonical__sum__merge sr) t1) (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) (happ (happ (h4/canonical/canonical__sum__merge sr) t1) t2)) (happ (happ (happ h4/canonical/Cons__monom c2) l2) (happ (happ (h4/canonical/canonical__sum__merge sr) (happ (happ (happ h4/canonical/Cons__monom c1) l1) t1)) t2))
% Assm [h4s_numRings_numu_u_canonicalu_u_sumu_u_mergeu_u_def]: h4/numRing/num__canonical__sum__merge = h4/canonical/canonical__sum__merge (h4/semi__ring/semi__ring0 h4/num/0 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) h4/arithmetic/_2B h4/arithmetic/_2A)
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_canonicals_varlistu_u_insertu_u_curriedu_u_def]: !x2 x1 x. happ (happ (h4/canonical/varlist__insert x) x1) x2 = happ h4/canonical/varlist__insert__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_canonicals_canonicalu_u_sumu_u_sizeu_u_defu_c2]: !f a1 a0. h4/canonical/canonical__sum__size f (happ (happ h4/canonical/Cons__varlist a0) a1) = happ (happ h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (happ (happ h4/arithmetic/_2B (h4/list/list__size h4/quote/index__size a0)) (h4/canonical/canonical__sum__size f a1))
% Assm [h4s_canonicals_canonicalu_u_sumu_u_caseu_u_defu_c0]: !v f1 f. h4/canonical/canonical__sum__CASE h4/canonical/Nil__monom v f f1 = v
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. happ (happ h4/arithmetic/_2B n) h4/num/0 = n
% Assm [h4s_canonicals_canonicalu_u_sumu_u_caseu_u_defu_c1]: !v f1 f a2 a1 a0. h4/canonical/canonical__sum__CASE (happ (happ (happ h4/canonical/Cons__monom a0) a1) a2) v f f1 = happ (happ (happ f a0) a1) a2
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (happ (happ h4/arithmetic/_2B m) n) (happ (happ h4/arithmetic/_2B m) p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = happ (happ h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. happ (happ h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) m = m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. happ (happ h4/arithmetic/_2B m) (happ (happ h4/arithmetic/_2B n) p) = happ (happ h4/arithmetic/_2B (happ (happ h4/arithmetic/_2B m) n)) p
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. happ (happ h4/arithmetic/_2B m) n = happ (happ h4/arithmetic/_2B n) m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. happ (happ h4/arithmetic/_2B h4/num/0) m = m
% Assm [h4s_arithmetics_ADDu_u_0]: !m. happ (happ h4/arithmetic/_2B m) h4/num/0 = m
% Assm [h4s_canonicals_canonicalu_u_sumu_u_caseu_u_defu_c2]: !v f1 f a1 a0. h4/canonical/canonical__sum__CASE (happ (happ h4/canonical/Cons__varlist a0) a1) v f f1 = happ (happ f1 a0) a1
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. happ (happ h4/arithmetic/_2B m) n = happ (happ h4/arithmetic/_2B n) m
% Goal: !i. happ h4/numRing/num__spolynom__normalize (happ h4/canonical/SPvar i) = happ (happ h4/canonical/Cons__varlist (h4/list/CONS i h4/list/NIL)) h4/canonical/Nil__monom
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_Q1373503,TV_Q1373499]: ![V_f, V_g]: (![V_x]: s(TV_Q1373499,happ(s(t_fun(TV_Q1373503,TV_Q1373499),V_f),s(TV_Q1373503,V_x))) = s(TV_Q1373499,happ(s(t_fun(TV_Q1373503,TV_Q1373499),V_g),s(TV_Q1373503,V_x))) => s(t_fun(TV_Q1373503,TV_Q1373499),V_f) = s(t_fun(TV_Q1373503,TV_Q1373499),V_g))).
fof(ah4s_canonicals_spolynomu_u_normalizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_sr, V_i]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_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))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_i),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_numRings_numu_u_spolynomu_u_normalizeu_u_def, axiom, s(t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),h4s_numrings_numu_u_spolynomu_u_normalize) = s(t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(t_h4s_nums_num),h4s_semiu_u_rings_semiu_u_ring0(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a)))))).
fof(ah4s_ringNorms_spolynomu_u_normalizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_r, V_i]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_spolynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_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))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_i),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_ringNorms_polynomu_u_normalizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_r, V_i]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_ringnorms_polynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r),s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar),s(t_h4s_quotes_index,V_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))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_i),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_canonicals_SPvar0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar) = s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical5)).
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_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_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_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_spolynomu_u_normalizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_sr, V_c]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,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_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
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_spolynomu_u_normalizeu_u_defu_c3, axiom, ![TV_u_27a]: ![V_sr, V_r, V_l]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_l))),s(t_h4s_canonicals_spolynom(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_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_canonicals_canonicalu_u_sumu_u_prod(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_r)))))).
fof(ah4s_canonicals_spolynomu_u_normalizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_sr, V_r, V_l]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_l))),s(t_h4s_canonicals_spolynom(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_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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_l))))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_r)))))).
fof(ah4s_ringNorms_ru_u_spolynomu_u_normalizeu_u_def, axiom, ![TV_u_27a]: ![V_r]: s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_spolynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))) = s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_canonicals_spolynomu_u_normalize(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_canonicalu_u_sumu_u_mergeu_u_def, axiom, ![TV_u_27a]: ![V_r]: 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_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_canonicals_canonicalu_u_sumu_u_merge(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_canonicalu_u_sumu_u_produ_u_def, axiom, ![TV_u_27a]: ![V_r]: 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_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_canonicals_canonicalu_u_sumu_u_prod(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_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_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_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_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_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_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_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_canonicals_SPconst0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst) = s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical6)).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical5u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical5),s(t_h4s_quotes_index,V_x))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_x),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_canonicals_spolynomu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_a))))) = s(t_h4s_canonicals_spolynom(TV_u_27a),V_a)).
fof(ah4s_canonicals_SPmult0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult) = s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical8)).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical6u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical6),s(TV_u_27a,V_x))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_canonicals_SPplus0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus) = s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical7)).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical8u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical8),s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_canonicals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typecanonical7u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_u_20u_40indu_u_typecanonical7),s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))) = s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_canonicals_spolynomu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27spolynomu_27]: (![V_a0u_270]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_a),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_a))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27spolynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_canonicals_u_20u_40indu_u_typecanonical10(s(t_h4s_canonicals_spolynom(TV_u_27a),h4s_canonicals_u_20u_40indu_u_typecanonical9(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r)))).
fof(ah4s_canonicals_interpu_u_spu_u_defu_c1, axiom, ![TV_u_27a]: ![V_vm, V_sr, V_i]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),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_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_canonicals_spolynomu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27b,h4s_canonicals_spolynomu_u_case(s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3))) = s(TV_u_27b,happ(s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_h4s_quotes_index,V_a)))).
fof(ah4s_numRings_numu_u_ringu_u_thmsu_c3, axiom, ![V_vm, V_i]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num),happ(s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_sp),s(t_h4s_quotes_varmap(t_h4s_nums_num),V_vm))),s(t_h4s_canonicals_spolynom(t_h4s_nums_num),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(t_h4s_nums_num)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_i))))) = s(t_h4s_nums_num,h4s_quotes_varmapu_u_find(s(t_h4s_quotes_index,V_i),s(t_h4s_quotes_varmap(t_h4s_nums_num),V_vm)))).
fof(ah4s_canonicals_spolynomu_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(t_h4s_nums_num,h4s_canonicals_spolynomu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_quotes_index,t_h4s_nums_num),h4s_quotes_indexu_u_size),s(t_h4s_quotes_index,V_a)))))).
fof(ah4s_canonicals_spolynomu_u_distinctu_c2, axiom, ![TV_u_27a]: ![V_a1, V_a0, V_a]: ~ (s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))).
fof(ah4s_canonicals_spolynomu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f3, V_f2, V_f1, V_f0]: ?[V_fn]: (![V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))))) = s(TV_u_27b,happ(s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f0),s(t_h4s_quotes_index,V_a))) & (![V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_a))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_a))) & (![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)))),V_f2),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))))),s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)))),V_f3),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))))),s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))))))).
fof(ah4s_canonicals_spolynomu_u_nchotomy, axiom, ![TV_u_27a]: ![V_ss]: (?[V_i]: s(t_h4s_canonicals_spolynom(TV_u_27a),V_ss) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_i))) | (?[V_a]: s(t_h4s_canonicals_spolynom(TV_u_27a),V_ss) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_a))) | (?[V_s, V_s0]: s(t_h4s_canonicals_spolynom(TV_u_27a),V_ss) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s0))) | ?[V_s, V_s0]: s(t_h4s_canonicals_spolynom(TV_u_27a),V_ss) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s0))))))).
fof(ah4s_canonicals_spolynomu_u_11u_c0, axiom, ![TV_u_27a]: ![V_au_27, V_a]: (s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_au_27))) <=> s(t_h4s_quotes_index,V_a) = s(t_h4s_quotes_index,V_au_27))).
fof(ah4s_canonicals_spolynomu_u_distinctu_c1, axiom, ![TV_u_27a]: ![V_a1, V_a0, V_a]: ~ (s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))))).
fof(ah4s_ringNorms_interpu_u_spu_u_defu_c1, axiom, ![TV_u_27a]: ![V_vm, V_r, V_i]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_sp(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_quotes_varmap(TV_u_27a),V_vm))),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),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_canonicals_spolynomu_u_caseu_u_cong, axiom, ![TV_u_27a,TV_u_27b]: ![V_f3u_27, V_f3, V_f2u_27, V_f2, V_f1u_27, V_f1, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_canonicals_spolynom(TV_u_27a),V_M) = s(t_h4s_canonicals_spolynom(TV_u_27a),V_Mu_27) & (![V_a]: (s(t_h4s_canonicals_spolynom(TV_u_27a),V_Mu_27) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) => s(TV_u_27b,happ(s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_h4s_quotes_index,V_a))) = s(TV_u_27b,happ(s(t_fun(t_h4s_quotes_index,TV_u_27b),V_fu_27),s(t_h4s_quotes_index,V_a)))) & (![V_a]: (s(t_h4s_canonicals_spolynom(TV_u_27a),V_Mu_27) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_a))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_a))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1u_27),s(TV_u_27a,V_a)))) & (![V_a0, V_a1]: (s(t_h4s_canonicals_spolynom(TV_u_27a),V_Mu_27) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))) => s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2u_27),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1)))) & ![V_a0, V_a1]: (s(t_h4s_canonicals_spolynom(TV_u_27a),V_Mu_27) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))) => s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3u_27),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1)))))))) => s(TV_u_27b,h4s_canonicals_spolynomu_u_case(s(t_h4s_canonicals_spolynom(TV_u_27a),V_M),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3))) = s(TV_u_27b,h4s_canonicals_spolynomu_u_case(s(t_h4s_canonicals_spolynom(TV_u_27a),V_Mu_27),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_fu_27),s(t_fun(TV_u_27a,TV_u_27b),V_f1u_27),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2u_27),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3u_27))))).
fof(ah4s_canonicals_spolynomu_u_distinctu_c0, axiom, ![TV_u_27a]: ![V_au_27, V_a]: ~ (s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_a))) = s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_au_27))))).
fof(ah4s_canonicals_spolynomu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((![V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_i)))))) & (![V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_a)))))) & (![V_s, V_s0]: ((p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s)))) & p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s0))))))) & ![V_s, V_s0]: ((p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s)))) & p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s0)))))))))) => ![V_s]: p(s(t_bool,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_bool),V_P),s(t_h4s_canonicals_spolynom(TV_u_27a),V_s)))))).
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_canonicals_datatypeu_u_spolynom, axiom, ![TV_u_27a]: ![V_spolynom]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),t_bool),happ(s(t_fun(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),t_fun(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),t_fun(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),t_fun(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),t_bool))),happ(s(t_fun(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),t_fun(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),t_fun(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),t_bool)))),V_spolynom),s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spvar))),s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst))),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus))),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult))))))).
fof(ah4s_canonicals_interpu_u_spu_u_defu_c2, axiom, ![TV_u_27a]: ![V_vm, V_sr, V_p2, V_p1]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_p1))),s(t_h4s_canonicals_spolynom(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_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,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),V_p1))))),s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),V_p2)))))).
fof(ah4s_canonicals_interpu_u_spu_u_defu_c3, axiom, ![TV_u_27a]: ![V_vm, V_sr, V_p2, V_p1]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_p1))),s(t_h4s_canonicals_spolynom(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_semiu_u_rings_semiu_u_ringu_u_srm(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),V_p1))))),s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),V_p2)))))).
fof(ah4s_canonicals_interpu_u_spu_u_defu_c0, axiom, ![TV_u_27a]: ![V_vm, V_sr, V_c]: s(TV_u_27a,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a),happ(s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_c))))) = s(TV_u_27a,V_c)).
fof(ah4s_semiu_u_rings_semiu_u_ringu_u_accessorsu_c3, 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_srm(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_f0)).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm2u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm2),s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_ringNorms_Popp0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_popp) = s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm4)).
fof(ah4s_ringNorms_Pconst0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pconst) = s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm1)).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm3u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm3),s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))))).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm4u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm4),s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))))).
fof(ah4s_ringNorms_Pmult0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pmult) = s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm3)).
fof(ah4s_ringNorms_Pplus0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_pplus) = s(t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_fun(t_h4s_ringNorms_polynom(TV_u_27a),t_h4s_ringNorms_polynom(TV_u_27a))),h4s_ringnorms_u_20u_40indu_u_typeringnorm2)).
fof(ah4s_ringNorms_Pvar0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_pvar) = s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm0)).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm1),s(TV_u_27a,V_x))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_ringNorms_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeringNorm0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_ringNorms_polynom(TV_u_27a),happ(s(t_fun(t_h4s_quotes_index,t_h4s_ringNorms_polynom(TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm0),s(t_h4s_quotes_index,V_x))) = s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_x),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))).
fof(ah4s_ringNorms_polynomu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27polynomu_27]: (![V_a0u_270]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,V_a),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,V_a))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a1)))))) | ?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),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_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),s(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_quotes_index,h4s_bools_arb),s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),t_bool),V_uu_27polynomu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),V_r)))).
fof(ah4s_ringNorms_polynomu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_ringNorms_polynom(TV_u_27a),h4s_ringnorms_u_20u_40indu_u_typeringnorm5(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_quotes_index,TV_u_27a)),h4s_ringnorms_u_20u_40indu_u_typeringnorm6(s(t_h4s_ringNorms_polynom(TV_u_27a),V_a))))) = s(t_h4s_ringNorms_polynom(TV_u_27a),V_a)).
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_numRings_numu_u_interpu_u_spu_u_def, axiom, s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num)),h4s_numrings_numu_u_interpu_u_sp) = s(t_fun(t_h4s_quotes_varmap(t_h4s_nums_num),t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_nums_num)),h4s_canonicals_interpu_u_sp(s(t_h4s_semiu_u_rings_semiu_u_ring(t_h4s_nums_num),h4s_semiu_u_rings_semiu_u_ring0(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a)))))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_canonicals_varlistu_u_insertu_u_defu_c2, axiom, ![TV_u_27a]: ![V_sr, 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_varlistu_u_insert(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),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_ru_u_interpu_u_spu_u_def, axiom, ![TV_u_27a]: ![V_r]: s(t_fun(t_h4s_quotes_varmap(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27a)),h4s_ringnorms_ru_u_interpu_u_sp(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_spolynom(TV_u_27a),TV_u_27a)),h4s_canonicals_interpu_u_sp(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_datatypeu_u_canonicalu_u_sum, axiom, ![TV_u_27a]: ![V_canonicalu_u_sum]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(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))),t_bool),happ(s(t_fun(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)))),t_fun(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))),t_bool)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),t_fun(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)))),t_fun(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))),t_bool))),V_canonicalu_u_sum),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)))),h4s_canonicals_consu_u_monom))),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))))))).
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_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: 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_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_ringNorms_spolynomu_u_normalizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_r, V_c]: s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),h4s_ringnorms_ru_u_spolynomu_u_normalize(s(t_h4s_rings_ring(TV_u_27a),V_r))),s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,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_canonicals_consu_u_monom),s(TV_u_27a,V_c))),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom)))).
fof(ah4s_canonicals_varlistu_u_insertu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_11]: (![V_l2u_27, V_varlistu_u_insertu_u_tupled, V_sr, 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(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_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(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(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_varlistu_u_insertu_u_tupled))),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),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))),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_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,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))),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(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_varlistu_u_insertu_u_tupled),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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(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_10]: (![V_varlistu_u_insertu_u_tupled, V_sr, 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),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_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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(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_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(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(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_varlistu_u_insertu_u_tupled))),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))) => ![V_uu_9]: (![V_c2, V_l2, V_varlistu_u_insertu_u_tupled, V_sr, 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(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_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(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_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(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(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_varlistu_u_insertu_u_tupled))),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_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))),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_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,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))),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(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_varlistu_u_insertu_u_tupled),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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(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_8]: (![V_c2, V_varlistu_u_insertu_u_tupled, V_sr, 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(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_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_8),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(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_varlistu_u_insertu_u_tupled))),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_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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(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_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(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_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(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(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_varlistu_u_insertu_u_tupled))),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))) => ![V_uu_7]: (![V_varlistu_u_insertu_u_tupled, V_sr, 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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_7),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),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(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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(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_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_8),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(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_varlistu_u_insertu_u_tupled))),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))) => ![V_uu_6]: (![V_varlistu_u_insertu_u_tupled, V_sr, V_l1, V_v3]: 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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_6),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),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_v3))) = 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_v3),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))),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))))),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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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_7),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),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_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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),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))))) => ![V_uu_5]: (![V_varlistu_u_insertu_u_tupled, V_sr, 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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_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_5),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),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_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_semiu_u_rings_semiu_u_ring(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(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_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_6),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),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))) => ![V_uu_4]: (![V_varlistu_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(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(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(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(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(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_varlistu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),s(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(t_h4s_lists_list(t_h4s_quotes_index),t_h4s_canonicals_canonicalu_u_sum(TV_u_27a)),V_v1),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_semiu_u_rings_semiu_u_ring(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(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_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_5),s(t_fun(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_varlistu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))) => ![V_uu_3]: (![V_varlistu_u_insertu_u_tupled, V_sr]: 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(t_h4s_semiu_u_rings_semiu_u_ring(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(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(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(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_varlistu_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(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(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(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(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(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_varlistu_u_insertu_u_tupled))),s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))) => ![V_uu_2]: (![V_varlistu_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(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(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(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(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_varlistu_u_insertu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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(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(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(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(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(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_varlistu_u_insertu_u_tupled))))) => ![V_uu_1]: (![V_varlistu_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(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(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(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(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_varlistu_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(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(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(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(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_varlistu_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(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(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(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(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(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(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_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(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(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(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(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(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(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(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_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(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(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(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(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(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(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(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(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_varlistu_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(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(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(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(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(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(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(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_numRings_numu_u_ringu_u_thmsu_c16, axiom, ![V_v8, V_v7]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_canonicalu_u_sumu_u_merge),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_nilu_u_monom))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),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_nums_num),V_v8))))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),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_nums_num),V_v8)))).
fof(ah4s_numRings_numu_u_ringu_u_thmsu_c22, axiom, ![V_l1]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_varlistu_u_insert),s(t_h4s_lists_list(t_h4s_quotes_index),V_l1))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_nilu_u_monom))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),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_nums_num),h4s_canonicals_nilu_u_monom)))).
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_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_semiu_u_rings_semiu_u_ringu_u_accessorsu_c1, axiom, ![TV_u_27a]: ![V_f0, V_f, V_a0, V_a]: 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),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_a0)).
fof(ah4s_canonicals_varlistu_u_insertu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t2, V_sr, 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_canonicals_varlistu_u_insert(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),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_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,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))),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_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_canonicals_varlistu_u_insert(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_t2)))))))).
fof(ah4s_canonicals_varlistu_u_insertu_u_defu_c0, axiom, ![TV_u_27a]: ![V_t2, V_sr, 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_canonicals_varlistu_u_insert(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),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_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,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))),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_canonicals_varlistu_u_insert(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_t2)))))))).
fof(ah4s_canonicals_spolynomu_u_caseu_u_defu_c3, axiom, ![TV_u_27b,TV_u_27a]: ![V_f3, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_canonicals_spolynomu_u_case(s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spmult),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3))) = s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1)))).
fof(ah4s_canonicals_spolynomu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_f3, V_f2, V_f1, V_f, V_a]: s(TV_u_27b,h4s_canonicals_spolynomu_u_case(s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_canonicals_spolynom(TV_u_27a)),h4s_canonicals_spconst),s(TV_u_27a,V_a))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_a)))).
fof(ah4s_canonicals_spolynomu_u_caseu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_f3, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_canonicals_spolynomu_u_case(s(t_h4s_canonicals_spolynom(TV_u_27a),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a)),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_h4s_canonicals_spolynom(TV_u_27a))),h4s_canonicals_spplus),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1))),s(t_fun(t_h4s_quotes_index,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2),s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f3))) = s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_canonicals_spolynom(TV_u_27a),t_fun(t_h4s_canonicals_spolynom(TV_u_27a),TV_u_27b)),V_f2),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a0))),s(t_h4s_canonicals_spolynom(TV_u_27a),V_a1)))).
fof(ah4s_numRings_numu_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_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_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_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_canonicals_varlistu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(t_h4s_nums_num),h4s_semiu_u_rings_semiu_u_ring0(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a)))))).
fof(ah4s_ringNorms_ru_u_varlistu_u_insertu_u_def, axiom, ![TV_u_27a]: ![V_r]: 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_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_varlistu_u_insert(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_canonicalu_u_sumu_u_mergeu_u_defu_c6, axiom, ![TV_u_27a]: ![V_v8, V_v7, V_sr]: 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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c5, axiom, ![TV_u_27a]: ![V_v6, V_v5, V_v4, V_sr]: 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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_sr, 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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_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,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c3, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_sr, 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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_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,h4s_semiu_u_rings_semiu_u_ringu_u_sr1(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))))),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),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_sr, 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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_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),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c4, axiom, ![TV_u_27a]: ![V_sr, V_s1]: 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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_mergeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_sr, 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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_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),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_sr))),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_numRings_numu_u_canonicalu_u_sumu_u_mergeu_u_def, axiom, s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_numrings_numu_u_canonicalu_u_sumu_u_merge) = s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_canonicals_canonicalu_u_sumu_u_merge(s(t_h4s_semiu_u_rings_semiu_u_ring(t_h4s_nums_num),h4s_semiu_u_rings_semiu_u_ring0(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a)))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (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_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_canonicals_varlistu_u_insertu_u_curriedu_u_def, axiom, ![TV_u_27a]: ![V_x2, V_x1, V_x]: 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_varlistu_u_insert(s(t_h4s_semiu_u_rings_semiu_u_ring(TV_u_27a),V_x))),s(t_h4s_lists_list(t_h4s_quotes_index),V_x1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_x2))) = 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(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_varlistu_u_insertu_u_tupled),s(t_h4s_pairs_prod(t_h4s_semiu_u_rings_semiu_u_ring(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_x),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_x1),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_x2)))))))).
fof(ah4s_canonicals_canonicalu_u_sumu_u_sizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_canonicals_canonicalu_u_sumu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),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))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(t_h4s_quotes_index,t_h4s_nums_num),h4s_quotes_indexu_u_size),s(t_h4s_lists_list(t_h4s_quotes_index),V_a0))))),s(t_h4s_nums_num,h4s_canonicals_canonicalu_u_sumu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_a1)))))))).
fof(ah4s_canonicals_canonicalu_u_sumu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f1, V_f]: s(TV_u_27b,h4s_canonicals_canonicalu_u_sumu_u_case(s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),h4s_canonicals_nilu_u_monom),s(TV_u_27b,V_v),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),TV_u_27b))),V_f),s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27b)),V_f1))) = s(TV_u_27b,V_v)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_canonicals_canonicalu_u_sumu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_canonicals_canonicalu_u_sumu_u_case(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_a0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_a1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_a2))),s(TV_u_27b,V_v),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),TV_u_27b))),V_f),s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27b)),V_f1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27b)),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),TV_u_27b))),V_f),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(t_h4s_quotes_index),V_a1))),s(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),V_a2)))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_canonicals_canonicalu_u_sumu_u_caseu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_canonicals_canonicalu_u_sumu_u_case(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))),s(TV_u_27b,V_v),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),TV_u_27b))),V_f),s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27b)),V_f1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(TV_u_27a),TV_u_27b)),V_f1),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_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_arithmetics_u_2b),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ch4s_numRings_numu_u_ringu_u_thmsu_c50, conjecture, ![V_i]: s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_spolynom(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),h4s_numrings_numu_u_spolynomu_u_normalize),s(t_h4s_canonicals_spolynom(t_h4s_nums_num),happ(s(t_fun(t_h4s_quotes_index,t_h4s_canonicals_spolynom(t_h4s_nums_num)),h4s_canonicals_spvar),s(t_h4s_quotes_index,V_i))))) = s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),happ(s(t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num)),happ(s(t_fun(t_h4s_lists_list(t_h4s_quotes_index),t_fun(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num))),h4s_canonicals_consu_u_varlist),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_cons(s(t_h4s_quotes_index,V_i),s(t_h4s_lists_list(t_h4s_quotes_index),h4s_lists_nil))))),s(t_h4s_canonicals_canonicalu_u_sum(t_h4s_nums_num),h4s_canonicals_nilu_u_monom)))).
