TSTP Solution File: ANA129^1 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ANA129^1 : TPTP v7.0.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n061.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.75MB
% OS : Linux 3.10.0-327.36.3.el7.x86_64
% CPULimit : 300s
% DateTime : Fri Jan 20 10:02:34 EST 2017
% Result : Timeout 289.78s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA129^1 : TPTP v7.0.0. Released v7.0.0.
% 0.02/0.10 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n061.star.cs.uiowa.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.30 % Memory : 32218.75MB
% 0.02/0.30 % OS : Linux 3.10.0-327.36.3.el7.x86_64
% 0.02/0.31 % CPULimit : 300
% 0.02/0.31 % DateTime : Fri Jan 20 05:18:33 CST 2017
% 0.02/0.31 % CPUTime :
% 0.08/0.53 Python 2.7.8
% 0.29/0.99 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af69c8b1dd0>, <kernel.Type object at 0x2af699b635f0>) of role type named thf_type_type/realax/real
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring type/realax/real:Type
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af699b949e0>, <kernel.Type object at 0x2af699b63320>) of role type named thf_type_type/nums/num
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring type/nums/num:Type
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af69c8b1950>, <kernel.DependentProduct object at 0x2af699b635f0>) of role type named thf_const_const/realax/real_pow
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/realax/real_pow:(type/realax/real->(type/nums/num->type/realax/real))
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af69c8b1dd0>, <kernel.DependentProduct object at 0x2af699b90b48>) of role type named thf_const_const/realax/real_of_num
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/realax/real_of_num:(type/nums/num->type/realax/real)
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af699b63560>, <kernel.DependentProduct object at 0x2af699b63098>) of role type named thf_const_const/realax/real_mul
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/realax/real_mul:(type/realax/real->(type/realax/real->type/realax/real))
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af699b63290>, <kernel.DependentProduct object at 0x2af699b90dd0>) of role type named thf_const_const/nums/SUC
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/nums/SUC:(type/nums/num->type/nums/num)
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af699b635f0>, <kernel.DependentProduct object at 0x2af699b907a0>) of role type named thf_const_const/nums/NUMERAL
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/nums/NUMERAL:(type/nums/num->type/nums/num)
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af699b63290>, <kernel.DependentProduct object at 0x2af699b90320>) of role type named thf_const_const/nums/BIT1
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/nums/BIT1:(type/nums/num->type/nums/num)
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af699b635f0>, <kernel.Constant object at 0x2af699b90b48>) of role type named thf_const_const/nums/_0
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/nums/_0:type/nums/num
% 0.29/0.99 FOF formula (<kernel.Constant object at 0x2af699b905f0>, <kernel.DependentProduct object at 0x2af699b90128>) of role type named thf_const_const/iterate/polynomial_function
% 0.29/0.99 Using role type
% 0.29/0.99 Declaring const/iterate/polynomial_function:((type/realax/real->type/realax/real)->Prop)
% 0.29/0.99 FOF formula (forall (P:(type/nums/num->Prop)), (((and (P (const/nums/NUMERAL const/nums/_0))) (forall (A:type/nums/num), ((P A)->(P (const/nums/SUC A)))))->(forall (A:type/nums/num), (P A)))) of role axiom named thm/nums/num_INDUCTION_
% 0.29/0.99 A new axiom: (forall (P:(type/nums/num->Prop)), (((and (P (const/nums/NUMERAL const/nums/_0))) (forall (A:type/nums/num), ((P A)->(P (const/nums/SUC A)))))->(forall (A:type/nums/num), (P A))))
% 0.29/0.99 FOF formula (forall (A:(type/realax/real->type/realax/real)) (A0:(type/realax/real->type/realax/real)), (((and (const/iterate/polynomial_function A)) (const/iterate/polynomial_function A0))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_mul (A A1)) (A0 A1)))))) of role axiom named thm/iterate/POLYNOMIAL_FUNCTION_MUL_
% 0.29/0.99 A new axiom: (forall (A:(type/realax/real->type/realax/real)) (A0:(type/realax/real->type/realax/real)), (((and (const/iterate/polynomial_function A)) (const/iterate/polynomial_function A0))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_mul (A A1)) (A0 A1))))))
% 0.29/0.99 FOF formula (forall (A:type/realax/real) (A0:type/nums/num), (((eq type/realax/real) ((const/realax/real_pow A) (const/nums/SUC A0))) ((const/realax/real_mul A) ((const/realax/real_pow A) A0)))) of role axiom named thm/realax/real_pow_1
% 0.29/0.99 A new axiom: (forall (A:type/realax/real) (A0:type/nums/num), (((eq type/realax/real) ((const/realax/real_pow A) (const/nums/SUC A0))) ((const/realax/real_mul A) ((const/realax/real_pow A) A0))))
% 0.29/0.99 FOF formula (forall (A:type/realax/real), (const/iterate/polynomial_function (fun (A0:type/realax/real)=> A))) of role axiom named thm/iterate/POLYNOMIAL_FUNCTION_CONST_
% 2.95/3.67 A new axiom: (forall (A:type/realax/real), (const/iterate/polynomial_function (fun (A0:type/realax/real)=> A)))
% 2.95/3.67 FOF formula (forall (A:type/realax/real), (((eq type/realax/real) ((const/realax/real_pow A) (const/nums/NUMERAL const/nums/_0))) (const/realax/real_of_num (const/nums/NUMERAL (const/nums/BIT1 const/nums/_0))))) of role axiom named thm/realax/real_pow_0
% 2.95/3.67 A new axiom: (forall (A:type/realax/real), (((eq type/realax/real) ((const/realax/real_pow A) (const/nums/NUMERAL const/nums/_0))) (const/realax/real_of_num (const/nums/NUMERAL (const/nums/BIT1 const/nums/_0)))))
% 2.95/3.67 FOF formula (forall (A:(type/realax/real->type/realax/real)) (A0:type/nums/num), ((const/iterate/polynomial_function A)->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0))))) of role conjecture named thm/iterate/POLYNOMIAL_FUNCTION_POW_
% 2.95/3.67 Conjecture to prove = (forall (A:(type/realax/real->type/realax/real)) (A0:type/nums/num), ((const/iterate/polynomial_function A)->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0))))):Prop
% 2.95/3.67 Parameter type/realax/real_DUMMY:type/realax/real.
% 2.95/3.67 We need to prove ['(forall (A:(type/realax/real->type/realax/real)) (A0:type/nums/num), ((const/iterate/polynomial_function A)->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))))']
% 2.95/3.67 Parameter type/realax/real:Type.
% 2.95/3.67 Parameter type/nums/num:Type.
% 2.95/3.67 Parameter const/realax/real_pow:(type/realax/real->(type/nums/num->type/realax/real)).
% 2.95/3.67 Parameter const/realax/real_of_num:(type/nums/num->type/realax/real).
% 2.95/3.67 Parameter const/realax/real_mul:(type/realax/real->(type/realax/real->type/realax/real)).
% 2.95/3.67 Parameter const/nums/SUC:(type/nums/num->type/nums/num).
% 2.95/3.67 Parameter const/nums/NUMERAL:(type/nums/num->type/nums/num).
% 2.95/3.67 Parameter const/nums/BIT1:(type/nums/num->type/nums/num).
% 2.95/3.67 Parameter const/nums/_0:type/nums/num.
% 2.95/3.67 Parameter const/iterate/polynomial_function:((type/realax/real->type/realax/real)->Prop).
% 2.95/3.67 Axiom thm/nums/num_INDUCTION_:(forall (P:(type/nums/num->Prop)), (((and (P (const/nums/NUMERAL const/nums/_0))) (forall (A:type/nums/num), ((P A)->(P (const/nums/SUC A)))))->(forall (A:type/nums/num), (P A)))).
% 2.95/3.67 Axiom thm/iterate/POLYNOMIAL_FUNCTION_MUL_:(forall (A:(type/realax/real->type/realax/real)) (A0:(type/realax/real->type/realax/real)), (((and (const/iterate/polynomial_function A)) (const/iterate/polynomial_function A0))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_mul (A A1)) (A0 A1)))))).
% 2.95/3.67 Axiom thm/realax/real_pow_1:(forall (A:type/realax/real) (A0:type/nums/num), (((eq type/realax/real) ((const/realax/real_pow A) (const/nums/SUC A0))) ((const/realax/real_mul A) ((const/realax/real_pow A) A0)))).
% 2.95/3.67 Axiom thm/iterate/POLYNOMIAL_FUNCTION_CONST_:(forall (A:type/realax/real), (const/iterate/polynomial_function (fun (A0:type/realax/real)=> A))).
% 2.95/3.67 Axiom thm/realax/real_pow_0:(forall (A:type/realax/real), (((eq type/realax/real) ((const/realax/real_pow A) (const/nums/NUMERAL const/nums/_0))) (const/realax/real_of_num (const/nums/NUMERAL (const/nums/BIT1 const/nums/_0))))).
% 2.95/3.67 Trying to prove (forall (A:(type/realax/real->type/realax/real)) (A0:type/nums/num), ((const/iterate/polynomial_function A)->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))))
% 2.95/3.67 Found eta_expansion0000:=(eta_expansion000 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) A00))))
% 2.95/3.67 Found (eta_expansion000 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 2.95/3.67 Found ((eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 2.95/3.67 Found (((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found eta_expansion0000:=(eta_expansion000 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) A00))))
% 5.95/6.61 Found (eta_expansion000 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found (((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found eta_expansion0000:=(eta_expansion000 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) A00))))
% 5.95/6.61 Found (eta_expansion000 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found (((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 5.95/6.61 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))):(((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0)))))))
% 6.18/6.88 Found (eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) b)
% 6.18/6.88 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) b)
% 6.18/6.88 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) b)
% 6.18/6.88 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))) b)
% 6.18/6.88 Found eq_ref00:=(eq_ref0 (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))):(((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0))))))
% 6.18/6.88 Found (eq_ref0 (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) b)
% 6.18/6.88 Found ((eq_ref Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) b)
% 6.18/6.88 Found ((eq_ref Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) b)
% 10.15/10.81 Found ((eq_ref Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))))) b)
% 10.15/10.81 Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 10.15/10.81 Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% 10.15/10.81 Found eq_sym as proof of b
% 10.15/10.81 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 10.15/10.81 Found x2 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 10.15/10.81 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))):(((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1))
% (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function
% (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))))))
% 10.15/10.81 Found (eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1))
% (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) b)
% 10.15/10.81 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1))
% (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) b)
% 10.15/10.81 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1))
% (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) b)
% 18.34/18.99 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1))
% (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))) b)
% 18.34/18.99 Found thm/nums/num_INDUCTION_:(forall (P:(type/nums/num->Prop)), (((and (P (const/nums/NUMERAL const/nums/_0))) (forall (A:type/nums/num), ((P A)->(P (const/nums/SUC A)))))->(forall (A:type/nums/num), (P A))))
% 18.34/18.99 Instantiate: b:=(forall (P:(type/nums/num->Prop)), (((and (P (const/nums/NUMERAL const/nums/_0))) (forall (A:type/nums/num), ((P A)->(P (const/nums/SUC A)))))->(forall (A:type/nums/num), (P A)))):Prop
% 18.34/18.99 Found thm/nums/num_INDUCTION_ as proof of b
% 18.34/18.99 Found x:(const/iterate/polynomial_function A)
% 18.34/18.99 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 18.34/18.99 Found x as proof of (P b)
% 18.34/18.99 Found eta_expansion000:=(eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/NUMERAL const/nums/_0))))
% 18.34/18.99 Found (eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) b)
% 28.72/29.39 Found ((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) b)
% 28.72/29.39 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) b)
% 28.72/29.39 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) b)
% 28.72/29.39 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0)))) b)
% 28.72/29.39 Found x:(const/iterate/polynomial_function A)
% 28.72/29.39 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 28.72/29.39 Found x as proof of (P b)
% 28.72/29.39 Found eq_ref00:=(eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 28.72/29.39 Found (eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 28.72/29.39 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 28.72/29.39 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 28.72/29.39 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 28.72/29.39 Found x:(const/iterate/polynomial_function A)
% 28.72/29.39 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 28.72/29.39 Found x as proof of (P f)
% 28.72/29.39 Found x:(const/iterate/polynomial_function A)
% 28.72/29.39 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 28.72/29.39 Found x as proof of (P f)
% 28.72/29.39 Found eq_ref00:=(eq_ref0 (f x0)):(((eq type/realax/real) (f x0)) (f x0))
% 28.72/29.39 Found (eq_ref0 (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 28.72/29.39 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 28.72/29.39 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 28.72/29.39 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 28.72/29.39 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/NUMERAL const/nums/_0))))
% 28.72/29.39 Found eq_ref00:=(eq_ref0 (f x0)):(((eq type/realax/real) (f x0)) (f x0))
% 28.72/29.39 Found (eq_ref0 (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 36.89/37.57 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 36.89/37.57 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 36.89/37.57 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL const/nums/_0)))
% 36.89/37.57 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/NUMERAL const/nums/_0))))
% 36.89/37.57 Found x:(const/iterate/polynomial_function A)
% 36.89/37.57 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 36.89/37.57 Found x as proof of (P f)
% 36.89/37.57 Found x:(const/iterate/polynomial_function A)
% 36.89/37.57 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 36.89/37.57 Found x as proof of (P f)
% 36.89/37.57 Found eq_ref00:=(eq_ref0 (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))):(((eq Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))
% 36.89/37.57 Found (eq_ref0 (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 36.89/37.57 Found ((eq_ref Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 36.89/37.57 Found ((eq_ref Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 36.89/37.57 Found ((eq_ref Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 36.89/37.57 Found eta_expansion000:=(eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) A00)))
% 38.92/39.59 Found (eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 38.92/39.59 Found ((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 38.92/39.59 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 38.92/39.59 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 38.92/39.59 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 38.92/39.59 Found eq_ref00:=(eq_ref0 b):(((eq (type/realax/real->type/realax/real)) b) b)
% 38.92/39.59 Found (eq_ref0 b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 38.92/39.59 Found ((eq_ref (type/realax/real->type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 38.92/39.59 Found ((eq_ref (type/realax/real->type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 38.92/39.59 Found ((eq_ref (type/realax/real->type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 38.92/39.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq type/realax/real) (f x1)) (f x1))
% 38.92/39.59 Found (eq_ref0 (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/SUC A00))))
% 38.92/39.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq type/realax/real) (f x1)) (f x1))
% 38.92/39.59 Found (eq_ref0 (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/SUC A00)))
% 38.92/39.59 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/SUC A00))))
% 38.92/39.59 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))))
% 42.26/42.90 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 42.26/42.90 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 42.26/42.90 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 42.26/42.90 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 42.26/42.90 Found eta_expansion000:=(eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) A00)))
% 42.26/42.90 Found (eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 42.26/42.90 Found ((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 42.26/42.90 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 42.26/42.90 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 42.26/42.90 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 42.26/42.90 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (type/realax/real->type/realax/real)) b) (fun (x:type/realax/real)=> (b x)))
% 42.26/42.90 Found (eta_expansion_dep00 b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 42.26/42.90 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 42.26/42.90 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 42.26/42.90 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 42.26/42.90 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 42.26/42.90 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))))
% 42.26/42.90 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 54.47/55.09 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 54.47/55.09 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 54.47/55.09 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 54.47/55.09 Found eq_ref00:=(eq_ref0 (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))):(((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))
% 54.47/55.09 Found (eq_ref0 (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 54.47/55.09 Found ((eq_ref Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 54.47/55.09 Found ((eq_ref Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 54.47/55.09 Found ((eq_ref Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 54.47/55.09 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))):(((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0))))))))
% 54.77/55.39 Found (eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) b)
% 54.77/55.39 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) b)
% 54.77/55.39 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) b)
% 54.77/55.39 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))))) b)
% 54.77/55.39 Found x300:=(x30 x2):(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found (x30 x2) as proof of (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found ((x3 A000) x2) as proof of (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found (fun (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2)) as proof of (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found (fun (x1:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2)) as proof of ((forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000))))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))
% 54.77/55.39 Found (fun (x1:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2)) as proof of ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->((forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000))))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 54.77/55.39 Found (and_rect00 (fun (x1:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2))) as proof of (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found ((and_rect0 (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))) (fun (x1:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2))) as proof of (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found (((fun (P:Type) (x1:((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->((forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))->P)))=> (((((and_rect (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) P) x1) x0)) (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))) (fun (x1:(const/iterate/polynomial_function (fun
% (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2))) as proof of (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found (fun (x2:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000))))=> (((fun (P:Type) (x1:((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->((forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))->P)))=> (((((and_rect (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) P) x1) x0)) (const/iterate/polynomial_function (fun
% (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))) (fun (x1:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2)))) as proof of (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))
% 54.77/55.39 Found (fun (A000:type/nums/num) (x2:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000))))=> (((fun (P:Type) (x1:((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->((forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))->P)))=> (((((and_rect (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) P) x1) x0)) (const/iterate/polynomial_function (fun
% (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))) (fun (x1:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2)))) as proof of ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))
% 54.77/55.39 Found (fun (A000:type/nums/num) (x2:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000))))=> (((fun (P:Type) (x1:((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->((forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))->P)))=> (((((and_rect (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) P) x1) x0)) (const/iterate/polynomial_function (fun
% (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))) (fun (x1:(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))) (x3:(forall (A0000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0000)))))))=> ((x3 A000) x2)))) as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 58.56/59.23 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))))
% 58.56/59.23 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.23 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.24 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.24 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.24 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))))
% 58.56/59.24 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.24 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.24 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.24 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 58.56/59.24 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))):(((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0))))))))
% 65.11/65.72 Found (eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) b)
% 65.11/65.72 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) b)
% 65.11/65.72 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) b)
% 65.11/65.72 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A0)))))))) b)
% 65.11/65.72 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 65.11/65.72 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 65.11/65.72 Found iff_sym as proof of b
% 65.11/65.72 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))))
% 65.11/65.72 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 65.11/65.72 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 65.11/65.72 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 77.82/78.49 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 77.82/78.49 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))))
% 77.82/78.49 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 77.82/78.49 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 77.82/78.49 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 77.82/78.49 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 77.82/78.49 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(P0 (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/SUC A00)))))
% 77.82/78.49 Found (eta_expansion000 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found ((eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found (((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))
% 77.82/78.49 Found (eq_ref00 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 77.82/78.49 Found eq_ref00:=(eq_ref0 (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))):(((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))
% 85.09/85.74 Found (eq_ref0 (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 85.09/85.74 Found ((eq_ref Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 85.09/85.74 Found ((eq_ref Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 85.09/85.74 Found ((eq_ref Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) as proof of (((eq Prop) (type/nums/num->((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))) b)
% 85.09/85.74 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))))
% 85.09/85.74 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 85.09/85.74 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 85.09/85.74 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 85.09/85.74 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 88.21/88.83 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))))
% 88.21/88.83 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 88.21/88.83 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 88.21/88.83 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 88.21/88.83 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A00))))
% 88.21/88.83 Found x:(const/iterate/polynomial_function A)
% 88.21/88.83 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 88.21/88.83 Found x as proof of (P b)
% 88.21/88.83 Found conj00:=(conj0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))):(((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))))
% (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))->((and ((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1))
% (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))))))))
% 91.01/91.61 Instantiate: b:=(((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0))))))
% (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))->((and ((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun
% (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))))))):Prop
% 91.01/91.61 Found conj00 as proof of b
% 91.01/91.61 Found eq_ref00:=(eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00)))))
% 91.01/91.61 Found (eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 91.01/91.61 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 97.31/97.99 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 97.31/97.99 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 97.31/97.99 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 97.31/97.99 Found x2 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 97.31/97.99 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))))
% 97.31/97.99 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found eq_ref000:=(eq_ref00 const/iterate/polynomial_function):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))))
% 97.31/97.99 Found (eq_ref00 const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01)))) const/iterate/polynomial_function) as proof of (P (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))
% 97.31/97.99 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 98.28/98.90 Found x2 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 98.28/98.90 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 98.28/98.90 Instantiate: b:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 98.28/98.90 Found iff_sym as proof of b
% 98.28/98.90 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))):(((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun
% (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))))))
% 98.28/98.90 Found (eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 98.28/98.90 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 98.28/98.90 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 104.72/105.33 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 104.72/105.33 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (type/realax/real->type/realax/real)) b) (fun (x:type/realax/real)=> (b x)))
% 104.72/105.33 Found (eta_expansion_dep00 b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 104.72/105.33 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 104.72/105.33 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 104.72/105.33 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 104.72/105.33 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 104.72/105.33 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/SUC A00))))
% 104.72/105.33 Found (eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 104.72/105.33 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/SUC A00))))
% 105.11/105.71 Found (eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 105.11/105.71 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (type/realax/real->type/realax/real)) b) (fun (x:type/realax/real)=> (b x)))
% 105.11/105.71 Found (eta_expansion_dep00 b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 105.11/105.71 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 105.11/105.71 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 109.82/110.48 Found conj00:=(conj0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))):((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0))))->((forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0))))) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/SUC A0)))))))))
% 109.82/110.48 Instantiate: b:=((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0))))->((forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL const/nums/_0))))) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0))))))))):Prop
% 109.82/110.48 Found conj00 as proof of b
% 109.82/110.48 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))
% 109.82/110.48 Found (eq_ref00 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 109.82/110.48 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 109.82/110.48 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 109.82/110.48 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 109.82/110.48 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(P0 (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/SUC A00)))))
% 109.82/110.48 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 109.82/110.48 Found ((eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 109.82/110.48 Found (((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 109.82/110.48 Found ((((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found ((((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))
% 124.41/125.03 Found (eq_ref00 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))->(P0 (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/SUC A00)))))
% 124.41/125.03 Found (eta_expansion000 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found ((eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found (((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found ((((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 124.41/125.03 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 124.41/125.03 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 124.41/125.03 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 124.41/125.03 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 124.41/125.03 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 131.90/132.52 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 131.90/132.52 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 131.90/132.52 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 131.90/132.52 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 131.90/132.52 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 131.90/132.52 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 131.90/132.52 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 131.90/132.52 Found x:(const/iterate/polynomial_function A)
% 131.90/132.52 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 131.90/132.52 Found x as proof of (P b)
% 131.90/132.52 Found x:(const/iterate/polynomial_function A)
% 131.90/132.52 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 131.90/132.52 Found x as proof of (P f)
% 131.90/132.52 Found x:(const/iterate/polynomial_function A)
% 131.90/132.52 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 131.90/132.52 Found x as proof of (P f)
% 131.90/132.52 Found eq_ref00:=(eq_ref0 (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))):(((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))
% 131.90/132.52 Found (eq_ref0 (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 131.90/132.52 Found ((eq_ref Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 131.90/132.52 Found ((eq_ref Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 131.90/132.52 Found ((eq_ref Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) as proof of (((eq Prop) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))) b)
% 141.20/141.84 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0)))))
% 141.20/141.84 Found (eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 141.20/141.84 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 141.20/141.84 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 141.20/141.84 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 141.20/141.84 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 141.20/141.84 Found eq_ref00:=(eq_ref0 ((const/realax/real_pow (A x0)) A00)):(((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) ((const/realax/real_pow (A x0)) A00))
% 141.20/141.84 Found (eq_ref0 ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 141.20/141.84 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 141.20/141.84 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 141.20/141.84 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 141.20/141.84 Found eq_ref00:=(eq_ref0 b):(((eq type/realax/real) b) b)
% 141.20/141.84 Found (eq_ref0 b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 141.20/141.84 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 141.20/141.84 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 141.20/141.84 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 141.20/141.84 Found eq_ref00:=(eq_ref0 ((const/realax/real_pow (A x0)) A00)):(((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) ((const/realax/real_pow (A x0)) A00))
% 141.20/141.84 Found (eq_ref0 ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found eq_ref00:=(eq_ref0 b):(((eq type/realax/real) b) b)
% 150.23/150.88 Found (eq_ref0 b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found eq_ref00:=(eq_ref0 ((const/realax/real_pow (A x0)) A00)):(((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) ((const/realax/real_pow (A x0)) A00))
% 150.23/150.88 Found (eq_ref0 ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found eq_ref00:=(eq_ref0 b):(((eq type/realax/real) b) b)
% 150.23/150.88 Found (eq_ref0 b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found eq_ref00:=(eq_ref0 ((const/realax/real_pow (A x0)) A00)):(((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) ((const/realax/real_pow (A x0)) A00))
% 150.23/150.88 Found (eq_ref0 ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found ((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) as proof of (((eq type/realax/real) ((const/realax/real_pow (A x0)) A00)) b)
% 150.23/150.88 Found eq_ref00:=(eq_ref0 b):(((eq type/realax/real) b) b)
% 150.23/150.88 Found (eq_ref0 b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found ((eq_ref type/realax/real) b) as proof of (((eq type/realax/real) b) ((const/realax/real_pow (A x0)) (const/nums/SUC A00)))
% 150.23/150.88 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 150.23/150.88 Found x2 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 156.81/157.46 Found eq_ref00:=(eq_ref0 (f x1)):(((eq type/realax/real) (f x1)) (f x1))
% 156.81/157.46 Found (eq_ref0 (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/SUC A00)))))
% 156.81/157.46 Found eq_ref00:=(eq_ref0 (f x1)):(((eq type/realax/real) (f x1)) (f x1))
% 156.81/157.46 Found (eq_ref0 (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found ((eq_ref type/realax/real) (f x1)) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (((eq type/realax/real) (f x1)) ((const/realax/real_pow (A x1)) (const/nums/NUMERAL (const/nums/SUC A00))))
% 156.81/157.46 Found (fun (x1:type/realax/real)=> ((eq_ref type/realax/real) (f x1))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/SUC A00)))))
% 156.81/157.46 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 156.81/157.46 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 156.81/157.46 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 156.81/157.46 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 156.81/157.46 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 156.81/157.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 156.81/157.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0)))))))
% 156.81/157.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0)))))))
% 156.81/157.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0)))))))
% 156.81/157.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A0)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A0)))))))
% 156.81/157.46 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 156.81/157.46 Found x2 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 156.81/157.46 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 171.12/171.74 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 171.12/171.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 171.12/171.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 171.12/171.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 171.12/171.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.12/171.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0))))))
% 171.12/171.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0))))))
% 171.12/171.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0))))))
% 171.12/171.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (type/nums/num->((const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0)))->(const/iterate/polynomial_function (fun (A10:type/realax/real)=> ((const/realax/real_pow (A A10)) A0))))))
% 171.12/171.74 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 171.12/171.74 Found x2 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 171.12/171.74 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 171.12/171.74 Found x2 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 171.12/171.74 Found thm/nums/num_INDUCTION_:(forall (P:(type/nums/num->Prop)), (((and (P (const/nums/NUMERAL const/nums/_0))) (forall (A:type/nums/num), ((P A)->(P (const/nums/SUC A)))))->(forall (A:type/nums/num), (P A))))
% 171.12/171.74 Instantiate: a:=(forall (P:(type/nums/num->Prop)), (((and (P (const/nums/NUMERAL const/nums/_0))) (forall (A:type/nums/num), ((P A)->(P (const/nums/SUC A)))))->(forall (A:type/nums/num), (P A)))):Prop
% 171.12/171.74 Found thm/nums/num_INDUCTION_ as proof of a
% 171.12/171.74 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))):(((eq Prop) (forall (A0:type/nums/num), (((and
% (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1))
% (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01)))))))))))
% 171.12/171.74 Found (eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and
% (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) b)
% 171.12/171.74 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and
% (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) b)
% 171.12/171.75 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and
% (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) b)
% 171.12/171.75 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and
% (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL A0)))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL (const/nums/SUC A0))))))) (forall (A01:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A01))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/SUC A01))))))))))) b)
% 185.24/185.86 Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% 185.24/185.86 Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% 185.24/185.86 Found eq_sym as proof of b
% 185.24/185.86 Found proj1:(forall (A:Prop) (B:Prop), (((and A) B)->A))
% 185.24/185.86 Instantiate: b:=(forall (A:Prop) (B:Prop), (((and A) B)->A)):Prop
% 185.24/185.86 Found proj1 as proof of b
% 185.24/185.86 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 185.24/185.86 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 185.24/185.86 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 185.24/185.86 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 185.24/185.86 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 185.24/185.86 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 185.24/185.86 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 207.51/208.14 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 207.51/208.14 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found eq_ref000:=(eq_ref00 P0):((P0 ((const/realax/real_pow (A x0)) A00))->(P0 ((const/realax/real_pow (A x0)) A00)))
% 207.51/208.14 Found (eq_ref00 P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found ((eq_ref0 ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found (((eq_ref type/realax/real) ((const/realax/real_pow (A x0)) A00)) P0) as proof of (P1 ((const/realax/real_pow (A x0)) A00))
% 207.51/208.14 Found x:(const/iterate/polynomial_function A)
% 207.51/208.14 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 207.51/208.14 Found x as proof of (P b)
% 207.51/208.14 Found x:(const/iterate/polynomial_function A)
% 207.51/208.14 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 207.51/208.14 Found x as proof of (P f)
% 207.51/208.14 Found x:(const/iterate/polynomial_function A)
% 207.51/208.14 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 207.51/208.14 Found x as proof of (P f)
% 207.51/208.14 Found x:(const/iterate/polynomial_function A)
% 207.51/208.14 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 207.51/208.14 Found x as proof of (P b)
% 207.51/208.14 Found x:(const/iterate/polynomial_function A)
% 207.51/208.14 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 207.51/208.14 Found x as proof of (P b)
% 207.51/208.14 Found x:(const/iterate/polynomial_function A)
% 207.51/208.14 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 207.51/208.14 Found x as proof of (P b)
% 207.51/208.14 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/SUC A00)))))
% 207.51/208.14 Found (eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 207.51/208.14 Found ((eta_expansion_dep0 (fun (x3:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 207.51/208.14 Found (((eta_expansion_dep type/realax/real) (fun (x3:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 221.15/221.79 Found (((eta_expansion_dep type/realax/real) (fun (x3:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 221.15/221.79 Found (((eta_expansion_dep type/realax/real) (fun (x3:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 221.15/221.79 Found eta_expansion000:=(eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0)))))
% 221.15/221.79 Found (eta_expansion00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 221.15/221.79 Found ((eta_expansion0 type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 221.15/221.79 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 221.15/221.79 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 221.15/221.79 Found (((eta_expansion type/realax/real) type/realax/real) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))) b)
% 221.15/221.79 Found x3:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 221.15/221.79 Found x3 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 221.15/221.79 Found eq_ref00:=(eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 221.15/221.79 Found (eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 221.15/221.79 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 226.74/227.37 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 226.74/227.37 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))) b)
% 226.74/227.37 Found eq_ref00:=(eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0)))))
% 226.74/227.37 Found (eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) b)
% 226.74/227.37 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) b)
% 226.74/227.37 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) b)
% 226.74/227.37 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC (const/nums/NUMERAL const/nums/_0))))) b)
% 226.74/227.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 226.74/227.37 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 226.74/227.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 226.74/227.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 226.74/227.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 226.74/227.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 226.74/227.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))))))
% 226.74/227.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))))))
% 230.84/231.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))))))
% 230.84/231.40 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL A0))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A00:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))))))))
% 230.84/231.40 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 230.84/231.40 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 230.84/231.40 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 230.84/231.40 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 230.84/231.40 Found ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 230.84/231.40 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 230.84/231.40 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of (forall (A:type/nums/num), ((((eq type/nums/num) A) (const/nums/SUC A))->(((eq type/nums/num) (const/nums/SUC A)) (const/nums/SUC (const/nums/SUC A)))))
% 230.84/231.40 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 230.84/231.40 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of (forall (A:type/nums/num), ((((eq type/nums/num) A) (const/nums/SUC A))->(((eq type/nums/num) (const/nums/SUC A)) (const/nums/SUC (const/nums/SUC A)))))
% 231.14/231.78 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of (forall (A:type/nums/num), ((((eq type/nums/num) A) (const/nums/SUC A))->(((eq type/nums/num) (const/nums/SUC A)) (const/nums/SUC (const/nums/SUC A)))))
% 231.14/231.78 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 231.14/231.78 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of (forall (A:type/nums/num), ((((eq type/nums/num) A) (const/nums/SUC A))->(((eq type/nums/num) (const/nums/SUC A)) (const/nums/SUC (const/nums/SUC A)))))
% 242.43/243.09 Found x:(const/iterate/polynomial_function A)
% 242.43/243.09 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 242.43/243.09 Found x as proof of (P b)
% 242.43/243.09 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 242.43/243.09 Instantiate: b:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% 242.43/243.09 Found conj as proof of b
% 242.43/243.09 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (type/realax/real->type/realax/real)) b) (fun (x:type/realax/real)=> (b x)))
% 242.43/243.09 Found (eta_expansion_dep00 b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found eq_ref00:=(eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 242.43/243.09 Found (eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 242.43/243.09 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 242.43/243.09 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 242.43/243.09 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 242.43/243.09 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (type/realax/real->type/realax/real)) b) (fun (x:type/realax/real)=> (b x)))
% 242.43/243.09 Found (eta_expansion_dep00 b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found ((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 242.43/243.09 Found (((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) b) as proof of (((eq (type/realax/real->type/realax/real)) b) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A00))))
% 246.74/247.32 Found eq_ref00:=(eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 246.74/247.32 Found (eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 246.74/247.32 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 246.74/247.32 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 246.74/247.32 Found ((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) b)
% 246.74/247.32 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/SUC A00)))))
% 246.74/247.32 Found (eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 246.74/247.32 Found ((eta_expansion_dep0 (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 246.74/247.32 Found (((eta_expansion_dep type/realax/real) (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 246.74/247.32 Found (((eta_expansion_dep type/realax/real) (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 246.74/247.32 Found (((eta_expansion_dep type/realax/real) (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 246.74/247.32 Found iff_sym:=(fun (A:Prop) (B:Prop) (H:((iff A) B))=> ((((conj (B->A)) (A->B)) (((proj2 (A->B)) (B->A)) H)) (((proj1 (A->B)) (B->A)) H))):(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A)))
% 246.74/247.32 Instantiate: a:=(forall (A:Prop) (B:Prop), (((iff A) B)->((iff B) A))):Prop
% 246.74/247.32 Found iff_sym as proof of a
% 246.74/247.32 Found x2:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 246.74/247.32 Found x2 as proof of b
% 255.25/255.89 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))):(((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC
% (const/nums/SUC A0)))))))))
% 255.25/255.89 Found (eq_ref0 (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) b)
% 255.25/255.89 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) b)
% 255.25/255.89 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) b)
% 255.25/255.89 Found ((eq_ref Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))))) b)
% 255.25/255.89 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))))
% 255.25/255.89 Found (eq_ref00 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))))
% 262.34/262.95 Found (eq_ref00 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found eq_ref000:=(eq_ref00 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))))
% 262.34/262.95 Found (eq_ref00 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found ((eq_ref0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found (((eq_ref (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))->(P0 (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) A00))))
% 262.34/262.95 Found (eta_expansion_dep000 P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found ((eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found (((eta_expansion_dep0 (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found ((((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found ((((eta_expansion_dep type/realax/real) (fun (x1:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00))) P0) as proof of (P1 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A00)))
% 262.34/262.95 Found x:(const/iterate/polynomial_function A)
% 262.34/262.95 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 262.34/262.95 Found x as proof of (P b)
% 262.34/262.95 Found eq_ref00:=(eq_ref0 (f x0)):(((eq type/realax/real) (f x0)) (f x0))
% 262.34/262.95 Found (eq_ref0 (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 262.34/262.95 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 270.23/270.81 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 270.23/270.81 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 270.23/270.81 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0)))))
% 270.23/270.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq type/realax/real) (f x0)) (f x0))
% 270.23/270.81 Found (eq_ref0 (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 270.23/270.81 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 270.23/270.81 Found ((eq_ref type/realax/real) (f x0)) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 270.23/270.81 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (((eq type/realax/real) (f x0)) ((const/realax/real_pow (A x0)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0))))
% 270.23/270.81 Found (fun (x0:type/realax/real)=> ((eq_ref type/realax/real) (f x0))) as proof of (forall (x:type/realax/real), (((eq type/realax/real) (f x)) ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/NUMERAL const/nums/_0)))))
% 270.23/270.81 Found x3:(forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 270.23/270.81 Found x3 as proof of (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))
% 270.23/270.81 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))):(((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) (fun (x:type/realax/real)=> ((const/realax/real_pow (A x)) (const/nums/NUMERAL (const/nums/SUC A00)))))
% 270.23/270.81 Found (eta_expansion_dep00 (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 270.23/270.81 Found ((eta_expansion_dep0 (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 270.23/270.81 Found (((eta_expansion_dep type/realax/real) (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 270.23/270.81 Found (((eta_expansion_dep type/realax/real) (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 270.23/270.81 Found (((eta_expansion_dep type/realax/real) (fun (x4:type/realax/real)=> type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) as proof of (((eq (type/realax/real->type/realax/real)) (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A00))))) b)
% 289.78/290.38 Found x:(const/iterate/polynomial_function A)
% 289.78/290.38 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 289.78/290.38 Found x as proof of (P b)
% 289.78/290.38 Found conj:(forall (A:Prop) (B:Prop), (A->(B->((and A) B))))
% 289.78/290.38 Instantiate: b:=(forall (A:Prop) (B:Prop), (A->(B->((and A) B)))):Prop
% 289.78/290.38 Found conj as proof of b
% 289.78/290.38 Found x:(const/iterate/polynomial_function A)
% 289.78/290.38 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 289.78/290.38 Found x as proof of (P f)
% 289.78/290.38 Found x:(const/iterate/polynomial_function A)
% 289.78/290.38 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 289.78/290.38 Found x as proof of (P f)
% 289.78/290.38 Found x:(const/iterate/polynomial_function A)
% 289.78/290.38 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 289.78/290.38 Found x as proof of (P f)
% 289.78/290.38 Found x:(const/iterate/polynomial_function A)
% 289.78/290.38 Instantiate: f:=A:(type/realax/real->type/realax/real)
% 289.78/290.38 Found x as proof of (P f)
% 289.78/290.38 Found x:(const/iterate/polynomial_function A)
% 289.78/290.38 Instantiate: b:=A:(type/realax/real->type/realax/real)
% 289.78/290.38 Found x as proof of (P b)
% 289.78/290.38 Found eq_ref00:=(eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))):(((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun
% (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000))))))))))
% 289.78/290.38 Found (eq_ref0 (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 289.78/290.39 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 289.78/290.39 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 290.92/291.49 Found ((eq_ref Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) as proof of (((eq Prop) (forall (A0:type/nums/num), (((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=>
% ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC A0)))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))->((and (const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/NUMERAL (const/nums/SUC (const/nums/SUC A0))))))) (forall (A000:type/nums/num), ((const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) A000)))->(const/iterate/polynomial_function (fun (A1:type/realax/real)=> ((const/realax/real_pow (A A1)) (const/nums/SUC A000)))))))))) b)
% 290.92/291.49 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 290.92/291.49 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 290.92/291.49 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 290.92/291.49 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 290.92/291.49 Found ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 290.92/291.49 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 290.92/291.49 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of (forall (A:type/nums/num), ((((eq type/nums/num) A) (const/nums/SUC A))->(((eq type/nums/num) (const/nums/SUC A)) (const/nums/SUC (const/nums/SUC A)))))
% 291.39/291.98 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of (forall (A:type/nums/num), ((((eq type/nums/num) A) (const/nums/SUC A))->(((eq type/nums/num) (const/nums/SUC A)) (const/nums/SUC (const/nums/SUC A)))))
% 291.39/291.98 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (fun (A1:type/nums/num)=> ((((eq_substitution0 type/nums/num) A1) (const/nums/SUC A1)) const/nums/SUC)) as proof of (forall (A:type/nums/num), ((((eq type/nums/num) A) (const/nums/SUC A))->(((eq type/nums/num) (const/nums/SUC A)) (const/nums/SUC (const/nums/SUC A)))))
% 291.39/291.98 Found eq_substitution01000:=(eq_substitution0100 const/nums/SUC):((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (eq_substitution0100 const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found ((eq_substitution010 (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found (((eq_substitution01 A1) (const/nums/SUC A1)) const/nums/SUC) as proof of ((((eq type/nums/num) A1) (const/nums/SUC A1))->(((eq type/nums/num) (const/nums/SUC A1)) (const/nums/SUC (const/nums/SUC A1))))
% 291.39/291.98 Found ((((eq_substitution0 type/nums/nu
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