Proof: Store 0
Let's prove the following theorem:
if the following are true:
- instruction #0 is
store src=3 addr=6 imm=0
- the PC at time 0 = 0
- value of cell 6 at time 0 = 7
- value of cell 3 at time 0 = 13
then value of cell 7 at time 1 = 13
Proof:
Given
1 | instruction #0 is store src=3 addr=6 imm=0 |
---|---|
2 | the PC at time 0 = 0 |
3 | value of cell 6 at time 0 = 7 |
4 | value of cell 3 at time 0 = 13 |
# | Claim | Reason |
---|---|---|
1 | value of cell ((value of cell 6 at time 0) + 0) at time (0 + 1) = value of cell 3 at time 0 | if instruction #0 is store src=3 addr=6 imm=0 and the PC at time 0 = 0, then value of cell ((value of cell 6 at time 0) + 0) at time (0 + 1) = value of cell 3 at time 0 |
2 | (value of cell 6 at time 0) + 0 = 7 + 0 | if value of cell 6 at time 0 = 7, then (value of cell 6 at time 0) + 0 = 7 + 0 |
3 | 7 + 0 = 7 | 7 + 0 = 7 |
4 | (value of cell 6 at time 0) + 0 = 7 | if (value of cell 6 at time 0) + 0 = 7 + 0 and 7 + 0 = 7, then (value of cell 6 at time 0) + 0 = 7 |
5 | value of cell ((value of cell 6 at time 0) + 0) at time (0 + 1) = value of cell 7 at time (0 + 1) | if (value of cell 6 at time 0) + 0 = 7, then value of cell ((value of cell 6 at time 0) + 0) at time (0 + 1) = value of cell 7 at time (0 + 1) |
6 | 0 + 1 = 1 | 0 + 1 = 1 |
7 | value of cell 7 at time (0 + 1) = value of cell 7 at time 1 | if 0 + 1 = 1, then value of cell 7 at time (0 + 1) = value of cell 7 at time 1 |
8 | value of cell 7 at time 1 = value of cell 3 at time 0 | if value of cell ((value of cell 6 at time 0) + 0) at time (0 + 1) = value of cell 7 at time (0 + 1) and value of cell 7 at time (0 + 1) = value of cell 7 at time 1 and value of cell ((value of cell 6 at time 0) + 0) at time (0 + 1) = value of cell 3 at time 0, then value of cell 7 at time 1 = value of cell 3 at time 0 |
9 | value of cell 7 at time 1 = 13 | if value of cell 7 at time 1 = value of cell 3 at time 0 and value of cell 3 at time 0 = 13, then value of cell 7 at time 1 = 13 |
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