For articulation point and bridge these following code is shown in "Competitive Programming-1: Steven Halim" (yes edition-1 because it is free):-

void articulationPointAndBridge(int u) {
  dfs_low[u] = dfs_num[u] = dfsNumberCounter++;      // dfs_low[u] <= dfs_num[u]
  for (int j = 0; j < (int)AdjList[u].size(); j++) {
    ii v = AdjList[u][j];
    if (dfs_num[v.first] == DFS_WHITE) {                          // a tree edge
      dfs_parent[v.first] = u;
      if (u == dfsRoot) rootChildren++;  // special case, count children of root

      articulationPointAndBridge(v.first);

      if (dfs_low[v.first] >= dfs_num[u])              // for articulation point
        articulation_vertex[u] = true;           // store this information first
      if (dfs_low[v.first] > dfs_num[u])                           // for bridge
        printf(" Edge (%d, %d) is a bridge\n", u, v.first);
      dfs_low[u] = min(dfs_low[u], dfs_low[v.first]);       // update dfs_low[u]
    }
    else if (v.first != dfs_parent[u])       // a back edge and not direct cycle
 [1]     dfs_low[u] = min(dfs_low[u], dfs_num[v.first]);       // update dfs_low[u] <---------------
} }

My doubt is [1]..In this line why are we using

1. dfs_low[u]=min(dfs_low[u], dfs_num[v.first]); Can anybody explain this..why are we using the dfs_num value not the dfs_low value in case of visited nodes? I mean what is wring with dfs_low[u]=min(dfs_low[u], dfs_num[v.first]);?

2. Second thing is when we are going in line [1] can't we say for sure that the v->first's dfs_num is smaller than dfs_num of u? (dfs_num is also considered as the dfs discovery time).

3. Third one is for verification--- In the bridge discovery case the condition is if (dfs_low[v.first] > dfs_num[u]) because we have to find another node among the child of u whose dfs_low is strictly greater than dfs_num otherwise we will select a single node as an edge --which is wrong! Is this line of logic correct?

Note: If anybody has any key insight in this algorithm he/she may help others (me also) users by posting it.

UPD-1: I have studied and searched about bridge tree and bridges. But no tutorial clearly states the answer of my questions. So anybody having any idea is requested to post here.