Proof: Compare Example Two
Let's prove the following theorem:
compare bit stack [ 0, [ 1, [ ] ] ] and bit stack [ 1, [ 1, [ ] ] ] = [ 0, [ 0, [ ] ] ]
Proof:
# | 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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