Correctness of Inorder traversal using stacks

Question

The code for inorder traversal without recursion that I'm writing is as follows:

// Iterative function to perform in-order traversal of the tree
void inorderIterative(Node *root)
{
    // create an empty stack
    stack<Node*> stack;

    // start from root node (set current node to root node)
    Node *curr = root;

    // if current node is null and stack is also empty, we're done
    while (!stack.empty() || curr != nullptr)
    {
        // if current node is not null, push it to the stack (defer it)
        // and move to its left child
        if (curr != nullptr)
        {
            stack.push(curr);
            curr = curr->left;
        }
        else
        {
            // else if current node is null, we pop an element from stack,
            // print it and finally set current node to its right child
            curr = stack.top();
            stack.pop();
            cout << curr->data << " ";

            curr = curr->right;
        }
    }}

Now, we need to prove the correctness of the code. Can anyone help me with it?