## The Principle of Green Tree Induction

Consider a tree structure.  We have a base node and out of each node is one or more baby nodes.

1) Base node is green.

2) At each node, green transfers to each baby node.

then

All nodes are green.

Green can mean a node is a member of a set or some condition is true at the node or something is defined at the node.

Green transfers to each baby node, means that if the node satisfies some condition, then each baby node coming out of that node satisfies the condition. The condition can contain the node index or other information.

If the condition contains the entire path traveled, we can modify this to a path induction principle.

1) Base node is green.

2) At each node, green transfers along each path to each path including each baby node.

Then

All paths through the tree are green.

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## About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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