deletions | additions       diff --git a/begin_equation_v_x__i_1__.tex b/begin_equation_v_x__i_1__.tex  index 795ee2e..ccfda46 100644  --- a/begin_equation_v_x__i_1__.tex  +++ b/begin_equation_v_x__i_1__.tex 
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\begin{equation}  v Err_{v,w}  = x_{i_1} \land v = y_{j_1} \\  w = x_{i_2} \land w = y_{j_2} \\  i_1 \left\{  \begin{matrix}  0, & j_1  < i_2 \\  v \neq w j_2  \\ 1, & j_1 > j_2  \end{matrix}\right.  \end{equation}