How to prove by induction that binary search tree is of AVL type?

Question

Could you please help how to prove by induction that current algorithm which tests if the binary search tree is of AVL type is correct?

int checkHeight(TreeNode root){
 if(root == null)       
    return 0;

 int leftHeight := checkHeight(root.left); 
 if(leftHeight == -1)   
    return -1;  

 int rightHeight := checkHeight(root.right); 
 if(rightHeight == -1)  
    return -1;

 int heightDiff := Math.abs(leftHeight - rightHeight);
 if(heightDiff > 1)         
    return -1;
 else
    return max(leftHeight, rightHeight) + 1;
}

I tried such proof.

Basis: root is null - return 0.

Induction step: if we have a tree, where B is a root then in the leaf levels the height is 0, moving to the top we take max(0, 0) = 0 and add 1. The height is correct. Calculating the difference between the height of left node and the height of the right one 0-0 = 0 we obtain that it is not bigger than 1. The result is 0+1 =1 - the correct height. For all binary search trees, such algorithm is correct.