Proof: Pre Extend Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = reverse and insert [ 0, [ ] ] to the beginning of [ 4, [ 2, [ ] ] ]	reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = reverse and insert [ 0, [ ] ] to the beginning of [ 4, [ 2, [ ] ] ] (Pre-extend)
2	reverse and insert [ 0, [ ] ] to the beginning of [ 4, [ 2, [ ] ] ] = reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ]	reverse and insert [ 0, [ ] ] to the beginning of [ 4, [ 2, [ ] ] ] = reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ] (Pre-extend)
3	reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ] = [ 0, [ 4, [ 2, [ ] ] ] ]	reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ] = [ 0, [ 4, [ 2, [ ] ] ] ] (Pre-extend (3))
4	reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ]	if reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = reverse and insert [ 0, [ ] ] to the beginning of [ 4, [ 2, [ ] ] ] and reverse and insert [ 0, [ ] ] to the beginning of [ 4, [ 2, [ ] ] ] = reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ], then reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ] (Transitive Property of Equality)
5	reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = [ 0, [ 4, [ 2, [ ] ] ] ]	if reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ] and reverse and insert [ ] to the beginning of [ 0, [ 4, [ 2, [ ] ] ] ] = [ 0, [ 4, [ 2, [ ] ] ] ], then reverse and insert [ 4, [ 0, [ ] ] ] to the beginning of [ 2, [ ] ] = [ 0, [ 4, [ 2, [ ] ] ] ] (Transitive Property of Equality)

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