While I was studying data structures on my own, I became curious about the remove algorithm in a binary heap. Here is the deletion algorithm for a max heap used in the textbook:

remove()
    item <- A[1];
    heapSize <- heapSize-1;
    i <- 2;
    while i <= heapSize do
        if i < heapSize and A[LEFT(i)] > A[RIGHT(i)]
            then largest <- LEFT(i);
            else largest <- RIGHT(i);
        if A[PARENT(largest)] > A[largest]
            then break;
        A[PARENT(largest)] <-> A[largest];
        i <- LEFT(largest);
    return item;

What I’m curious about is the second line from the bottom.

Why does it assign LEFT(largest) instead of largest to i?

If the node at A[PARENT(largest)] has a smaller value than the child node, and that value is exchanged with the larger child node, shouldn’t largest be assigned to i and then compared with the next child? The pseudocode above seems to make two level jumps in one iteration of the loop… How could this be correct?