Proof: Push Stack Example

Let's prove the following theorem:

Proof:

Proof Table

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

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