Proof: Push Stack Example

Let's prove the following theorem:

result of dumping [ 4, [ 0, [ ] ] ] to [ 2, [ ] ] = [ 0, [ 4, [ 2, [ ] ] ] ]

Proof:

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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, [ ] ] ]
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, [ ] ] ] ]
3 result of dumping [ ] to [ 0, [ 4, [ 2, [ ] ] ] ] = [ 0, [ 4, [ 2, [ ] ] ] ] result of dumping [ ] to [ 0, [ 4, [ 2, [ ] ] ] ] = [ 0, [ 4, [ 2, [ ] ] ] ]
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, [ ] ] ] ]
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, [ ] ] ] ]
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