Proof: Compare Example Two

Let's prove the following theorem:

compare bit stack [ 0, [ 1, [ ] ] ] and bit stack [ 1, [ 1, [ ] ] ] = [ 0, [ 0, [ ] ] ]

Proof:

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Proof Table
# Claim Reason
1 compare bit stack [ 1, [ ] ] and bit stack [ 1, [ ] ] = [ 1, [ 0, [ ] ] ] compare bit stack [ 1, [ ] ] and bit stack [ 1, [ ] ] = [ 1, [ 0, [ ] ] ]
2 compare bit stack [ 0, [ 1, [ ] ] ] and bit stack [ 1, [ 1, [ ] ] ] = compare bit 0 and bit 1 if compare bit stack [ 1, [ ] ] and bit stack [ 1, [ ] ] = [ 1, [ 0, [ ] ] ], then compare bit stack [ 0, [ 1, [ ] ] ] and bit stack [ 1, [ 1, [ ] ] ] = compare bit 0 and bit 1
3 compare bit 0 and bit 1 = [ 0, [ 0, [ ] ] ] compare bit 0 and bit 1 = [ 0, [ 0, [ ] ] ]
4 compare bit stack [ 0, [ 1, [ ] ] ] and bit stack [ 1, [ 1, [ ] ] ] = [ 0, [ 0, [ ] ] ] if compare bit stack [ 0, [ 1, [ ] ] ] and bit stack [ 1, [ 1, [ ] ] ] = compare bit 0 and bit 1 and compare bit 0 and bit 1 = [ 0, [ 0, [ ] ] ], then compare bit stack [ 0, [ 1, [ ] ] ] and bit stack [ 1, [ 1, [ ] ] ] = [ 0, [ 0, [ ] ] ]

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