In the proof of the predecessor subgraph property (page 14 of the following notes)http://www.cs.sfu.ca/CourseCentral/307/binay/shortestpath.pdf$d[v_i] \geq d[v_{i-1}]+w(v_{i-1},v_{i})$ is assumed true. Why is this? Shouldn't it be the other inequality:  $d[v_i] \leq d[v_{i-1}]+w(v_{i-1},v_{i})$ by triangle inequality?
Predecessor-subgraph property
graphs;algorithm analysis