Proof: Minimum Example

Let's prove the following theorem:

minimum value of stack [ 3, [ 2, [ 1, [ ] ] ] ] = 1

In this example, we prove that the minimum value of [3, [2, [1, []]]] is 1. We start with just the innermost element, which is 1. We know that the minimum of [1, []] is 1.

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

Using the same reasoning as above, we conclude that the minimum of [3, [2, [1, []]]] is 1.

Proof:

View as a tree | View dependent proofs | Try proving it

Proof Table

#	Claim	Reason
1	minimum value of stack [ 1, [ ] ] = 1	minimum value of stack [ 1, [ ] ] = 1 (Minimum Of A Single Element List)
2	2 > 1	2 > 1 (Fixed Value Statement)
3	2 > minimum value of stack [ 1, [ ] ] = 2 > 1	if minimum value of stack [ 1, [ ] ] = 1, then 2 > minimum value of stack [ 1, [ ] ] = 2 > 1 (Substitution)
4	2 > minimum value of stack [ 1, [ ] ]	if 2 > 1 and 2 > minimum value of stack [ 1, [ ] ] = 2 > 1, then 2 > minimum value of stack [ 1, [ ] ] (Truth Propagation Property 2)
5	minimum value of stack [ 2, [ 1, [ ] ] ] = minimum value of stack [ 1, [ ] ]	if 2 > minimum value of stack [ 1, [ ] ], then minimum value of stack [ 2, [ 1, [ ] ] ] = minimum value of stack [ 1, [ ] ] (Greater Than Minimum Property)
6	minimum value of stack [ 2, [ 1, [ ] ] ] = 1	if minimum value of stack [ 2, [ 1, [ ] ] ] = minimum value of stack [ 1, [ ] ] and minimum value of stack [ 1, [ ] ] = 1, then minimum value of stack [ 2, [ 1, [ ] ] ] = 1 (Transitive Property of Equality)
7	3 > 1	3 > 1 (Fixed Value Statement)
8	3 > minimum value of stack [ 2, [ 1, [ ] ] ] = 3 > 1	if minimum value of stack [ 2, [ 1, [ ] ] ] = 1, then 3 > minimum value of stack [ 2, [ 1, [ ] ] ] = 3 > 1 (Substitution)
9	3 > minimum value of stack [ 2, [ 1, [ ] ] ]	if 3 > 1 and 3 > minimum value of stack [ 2, [ 1, [ ] ] ] = 3 > 1, then 3 > minimum value of stack [ 2, [ 1, [ ] ] ] (Truth Propagation Property 2)
10	minimum value of stack [ 3, [ 2, [ 1, [ ] ] ] ] = minimum value of stack [ 2, [ 1, [ ] ] ]	if 3 > minimum value of stack [ 2, [ 1, [ ] ] ], then minimum value of stack [ 3, [ 2, [ 1, [ ] ] ] ] = minimum value of stack [ 2, [ 1, [ ] ] ] (Greater Than Minimum Property)
11	minimum value of stack [ 3, [ 2, [ 1, [ ] ] ] ] = 1	if minimum value of stack [ 3, [ 2, [ 1, [ ] ] ] ] = minimum value of stack [ 2, [ 1, [ ] ] ] and minimum value of stack [ 2, [ 1, [ ] ] ] = 1, then minimum value of stack [ 3, [ 2, [ 1, [ ] ] ] ] = 1 (Transitive Property of Equality)

Comments

Please log in to add comments