Proof: Byte 126 Stays the Same 11
Let's prove the following theorem:
if the following are true:
- instruction #17 is
load dst=3 addr=1 imm=1
- the PC at time 11 = 17
- value of cell 126 at time 11 = 3
then value of cell 126 at time 12 = 3
Proof:
Given
1 | instruction #17 is load dst=3 addr=1 imm=1 |
---|---|
2 | the PC at time 11 = 17 |
3 | value of cell 126 at time 11 = 3 |
# | Claim | Reason |
---|---|---|
1 | not (126 = 3) | not (126 = 3) |
2 | value of cell 126 at time (11 + 1) = value of cell 126 at time 11 | if instruction #17 is load dst=3 addr=1 imm=1 and the PC at time 11 = 17 and not (126 = 3), then value of cell 126 at time (11 + 1) = value of cell 126 at time 11 |
3 | 11 + 1 = 12 | 11 + 1 = 12 |
4 | value of cell 126 at time (11 + 1) = value of cell 126 at time 12 | if 11 + 1 = 12, then value of cell 126 at time (11 + 1) = value of cell 126 at time 12 |
5 | value of cell 126 at time 12 = value of cell 126 at time 11 | if value of cell 126 at time (11 + 1) = value of cell 126 at time 12 and value of cell 126 at time (11 + 1) = value of cell 126 at time 11, then value of cell 126 at time 12 = value of cell 126 at time 11 |
6 | value of cell 126 at time 12 = 3 | if value of cell 126 at time 12 = value of cell 126 at time 11 and value of cell 126 at time 11 = 3, then value of cell 126 at time 12 = 3 |
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