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Let be a Weil algebra. The bijection between all natural operators lifting vector fields from -manifolds to the bundle functor of Weil contact elements and the subalgebra of fixed elements of the Weil algebra is determined and the bijection between all natural affinors on and is deduced. Furthermore, the rigidity of the functor is proved. Requisite results about the structure of are obtained by a purely algebraic approach, namely the existence of nontrivial is discussed.
This article formalizes the proof of Niven’s theorem [12] which states that if x/π and sin(x) are both rational, then the sine takes values 0, ±1/2, and ±1. The main part of the formalization follows the informal proof presented at Pr∞fWiki (https://proofwiki.org/wiki/Niven’s_Theorem#Source_of_Name). For this proof, we have also formalized the rational and integral root theorems setting constraints on solutions of polynomial equations with integer coefficients [8, 9].
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