Proof: Maximum Example

Let's prove the following theorem:

In this example, we prove that the maximum value of [2, [1, []]] is 2. We start with just the innermost element, which is 1. We know that the maximum of [1, []] is 1.

Next, we know that 2 is greater than the maximum of [1, []] since the maximum of [1, []] is 1 and 2 > 1. Then we conclude that the maximum of [2, [1, []]] is 2.

Proof:

Proof Table

#	Claim	Reason
1	maximum value in stack [ 1, [ ] ] = 1	maximum value in stack [ 1, [ ] ] = 1 (Maximum Of A Single Element List)
2	2 > 1	2 > 1 (Fixed Value Statement)
3	2 > maximum value in stack [ 1, [ ] ] = 2 > 1	if maximum value in stack [ 1, [ ] ] = 1, then 2 > maximum value in stack [ 1, [ ] ] = 2 > 1 (Substitution)
4	2 > maximum value in stack [ 1, [ ] ]	if 2 > 1 and 2 > maximum value in stack [ 1, [ ] ] = 2 > 1, then 2 > maximum value in stack [ 1, [ ] ] (Truth Propagation Property 2)
5	maximum value in stack [ 2, [ 1, [ ] ] ] = 2	if 2 > maximum value in stack [ 1, [ ] ], then maximum value in stack [ 2, [ 1, [ ] ] ] = 2 (Greater Than Maximum Property)

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