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NANANANANANANANANANANAA doubtful point on Thm 12.7 on 《The Topology of Fibre bundles》 pp. 56

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The construction is letting ${0V_i,1V_j}$ to be the coordinate neighborhoods for XxI. Then ${g_{10,ij}=(g_{01,ji})^{-1}}$. However, when I try to verify the transitive law for
$V_{1,i}\cap V_{0,j}\cap V_{0,k}$, the identity leads to $h_{0,jk}(x)=h_{1,jk}(x)$ which is not right in general.
    Post Closed as "too localized" by Ryan Budney, Deane Yang, David Roberts, Andrej Bauer, Daniel Litt

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The construction is letting ${0V_i,1V_j}$ to be the coordinate neighborhoods for XxI. Then ${g_{10,ij}=(g_{01,ji})^{-1}}$. However, when I try to verify the transitive law for
$V_{1,i}\cap V_{0,j}\cap V_{0,k}$, the identity leads to $h_{0,jk}(x)=h_{1,jk}(x)$ which is not right in general.

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