deletions | additions       diff --git a/Making_a_Spanner_Proof_by__.md b/Making_a_Spanner_Proof_by__.md  index 98aedb7..ec45302 100644  --- a/Making_a_Spanner_Proof_by__.md  +++ b/Making_a_Spanner_Proof_by__.md 
...
To prove this, we adopt the following strategy for constructing a t-path between any two points `i` and `j`. Assume WLOG we start from `i`. At every step, we choose the edge whose end-point lies in the same segment as `j`.  Let `k` be the point added as part of our inductive step. For all pair of points \(i,j | \ |\  i\neq k, j\neq k\) We refer to this path as \((i, v_1, v_2 \dots, v_{p-1}, j)\).