deletions | additions       diff --git a/Making_a_Spanner_Proof_by__.md b/Making_a_Spanner_Proof_by__.md  index 64170cd..2dedf07 100644  --- a/Making_a_Spanner_Proof_by__.md  +++ b/Making_a_Spanner_Proof_by__.md 
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Furthermore we claim that \(|ij| < |ik|\). This holds by the way we construct our graph. `k` is clearly in the same segment as `k`. Therefore,.... (2).  As such, from (1) we have such: