Is this A* pseudocode taking the condition of admisible ad consistent heuristic function hypothesis for granted?

Question

This is the pseudocode for A* from wiki:

function reconstruct_path(cameFrom, current)
    total_path := {current}
    while current in cameFrom.Keys:
        current := cameFrom[current]
        total_path.prepend(current)
    return total_path

// A* finds a path from start to goal.
// h is the heuristic function. h(n) estimates the cost to reach goal from node n.
function A_Star(start, goal, h)
    // The set of discovered nodes that may need to be (re-)expanded.
    // Initially, only the start node is known.
    // This is usually implemented as a min-heap or priority queue rather than a hash-set.
    openSet := {start}

    // For node n, cameFrom[n] is the node immediately preceding it on the cheapest path from start
    // to n currently known.
    cameFrom := an empty map

    // For node n, gScore[n] is the cost of the cheapest path from start to n currently known.
    gScore := map with default value of Infinity
    gScore[start] := 0

    // For node n, fScore[n] := gScore[n] + h(n). fScore[n] represents our current best guess as to
    // how cheap a path could be from start to finish if it goes through n.
    fScore := map with default value of Infinity
    fScore[start] := h(start)

    while openSet is not empty
        // This operation can occur in O(Log(N)) time if openSet is a min-heap or a priority queue
        current := the node in openSet having the lowest fScore[] value
        if current = goal
            return reconstruct_path(cameFrom, current)

        openSet.Remove(current)
        for each neighbor of current
            // d(current,neighbor) is the weight of the edge from current to neighbor
            // tentative_gScore is the distance from start to the neighbor through current
            tentative_gScore := gScore[current] + d(current, neighbor)
            if tentative_gScore < gScore[neighbor]
                // This path to neighbor is better than any previous one. Record it!
                cameFrom[neighbor] := current
                gScore[neighbor] := tentative_gScore
                fScore[neighbor] := tentative_gScore + h(neighbor)
                if neighbor not in openSet
                    openSet.add(neighbor)

    // Open set is empty but goal was never reached
    return failure

And this is another pseudocode that i found:

 function A*(start,goal)
 closedset := the empty set                 % The set of nodes already evaluated.     
 openset := set containing the initial node % The set of tentative nodes to be evaluated.
 g_score[start] := 0                        % Distance from start along optimal path.
 came_from := the empty map                 % The map of navigated nodes.
 h_score[start] := heuristic_estimate_of_distance(start, goal)
 f_score[start] := h_score[start]           % Estimated total distance from start to goal through y.
 while openset is not empty
     x := the node in openset having the lowest f_score[] value
     if x = goal
         return reconstruct_path(came_from,goal)
     remove x from openset
     add x to closedset
     foreach y in neighbor_nodes(x)
         if y in closedset
             continue
         tentative_g_score := g_score[x] + dist_between(x,y)
         
         if y not in openset
             add y to openset
            
             tentative_is_better := true
         elseif tentative_g_score < g_score[y]
             tentative_is_better := true
         else
             tentative_is_better := false
         if tentative_is_better = true
             came_from[y] := x
             g_score[y] := tentative_g_score
             h_score[y] := heuristic_estimate_of_distance(y, goal)
             f_score[y] := g_score[y] + h_score[y]
 return failure

 function reconstruct_path(came_from,current_node)
     if came_from[current_node] is set
         p = reconstruct_path(came_from,came_from[current_node])
         return (p + current_node)
     else
         return the empty path

The two pseudocodes do the same thing, but the first one is simpler. Is the first pseudocode simpler because it is assuming that the heuristic function is admissible(never overestimates the actual cost to get to the goal) and consistent (h(x) ≤ d(x, y) + h(y))?