who can give me a solution to my doubt. It is concerning about BINARY TREES:

The theorem says:

Def 1: A binary tree is balanced if for each node it holds that the number of inner nodes in the left subtree and the number of inner nodes in the right subtree differ by at most 1.

Def 2: A binary tree is balanced if for any two leaves the difference of the depth is at most 1.

My doubt is the following: if every tree that statisfy Def. 1 also statisfy Def. 2? is that true? And this is valid also in the other way round?

Thanks for helping me!