Property of Tensor Satisfying Binary Law 2

I have already reported “Property of Tensor Satisfying Binary Law”. This article is the article that I revise the contents of “Property of Tensor Satisfying Binary Law”, and increase the report about new characteristics. We may arrive at the deeper understanding in this about “Property of Tensor Satisfying Binary Law”.


Introduction
I have already reported "Property of Tensor Satisfying Binary Law" [1]. This article is the article that I revise the contents of "Property of Tensor Satisfying Bi-
x x x x µ µ ν ν ∂ = ∂ Definition 16 When the next conversion equation is established, x µ is covariant components of a tensor of the first rank [4].
x x x x ν µ ν µ ∂ = ∂ Definition 17 When the next conversion equation is established, x µν is contravariant components of a tensor of the second rank [4].
x x x x x x µ ν µν σλ σ λ ∂ ∂ = ∂ ∂ Definition 18 When the next conversion equation is established, x µν is covariant components of a tensor of the second rank [4]. x When the next conversion equation is established, x µ ν is components of the mixed tensor of the second rank [4].
∂ ∂ Definition 20 When the next conversion equation is established, x µ νσ is components of the mixed tensor of the third rank of the second rank covariant in the first rank contravariant [4]. x from (1), (77).

About Covariant Derivative for the Vector in Tensor Satisfying Binary Law
Proof: If all coordinate systems satisfy Binary Law, I get ; 1 2 from Definition 10. (4) must rewrite it in by (4) being a tensor equation. The dummy index has an invariable property for consideration of Binary Law. In other words, the index which was dummy index in Definition 10 is dummy index in (5). I get the conclusion that (5) doesn't satisfy Binary Law from Definition 6. I get the conclusion that Definition 10 isn't an equation of the tensor satisfying Binary Law because (5) doesn't satisfy Binary Law.
I rewrite one existing index ν in each term of (5) in index µ using Definition 2 and get ; 1 , 2 I rewrite one existing index ν in each term of (5) in index µ using Definition 4 and get in consideration of Definition 7 for (7). Because the second term of the right side of (8) doesn't exist, can rewrite (8) using Definition 4. In addition, ; x µ ν can't rewrite ; x µ µ of (6) using Definition 2 because the second term of the right side exists in (6).
The dummy index has an invariable property for consideration of Binary Law.
In other words, the index which was dummy index in Definition 11 is dummy index in (12), (13). I get the conclusion that (12), (13) doesn't satisfy Binary Law from Definition 6. I get the conclusion that Definition 11 isn't an equation of the tensor satisfying Binary Law because (12), (13) doesn't satisfy Binary Law.
I rewrite one existing index ν in each term of (12), (13) in index µ using Definition 4 and get in consideration of Definition 7 for (14). Because the second term of the right side of (15) doesn't exist, can rewrite (15) using Definition 4. I rewrite one existing index ν in each term of (12), (13) in index µ using Definition 2 and get by (17) in consideration of Definition 7 for (21). Because the second term of the right side of (22) doesn't exist,

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.