I have a problem with understanding the following mathematical model of the TSP. Given that the TSP is:
$$\min \sum_{i,j\in N} d_{i,j} \cdot x_{i,j}$$
subjected to:
$$\begin{array}{rrrr}\sum_{j\in N}x_{i,j}&=&1&\forall i \in N\\\ \sum_{i\in N}x_{i,j} &=& 1 & \forall j \in N\\ u_{i}+1 &\leq& u_{j} + |N| \cdot (1-x_{i,j})&\forall i,j \in N: i\neq j, j\neq 1\\ u_{1} &=& 1& \forall i \in N \\ x_{i,i} &=& 0 &\forall i \in N \\ x_{i,j} &\in& \{0,1\}&\forall i,j \in N\\ u_{i} &\in& \mathbb{Z}_{+} &\forall i \in N\end{array}$$
Where $x_{i,j}$ is an integer, that determines whether the path is selected in the solution and $u_{i}$ is the position of city $i$ along the tour. $N$ is a set of cities and $d_{i,j}$ is the distance between city $i$ and $j$.
I have a hard time understanding the constraint $u_{i} + 1 \leq u_{j} + |N| (1-x_{i,j})$. I do not see the inuition behind, why this constraint would eliminate the subtours. Suppose, I have three tours (see in the figure below). The left circle is a solution to the TSP, while the right one is one with only the subtours. I am not sure how the constraint would prohibit a subtour from forming, as $|N|$ seems to be big enough to allow for subtours if my $u_{j} = 1$.