Proof: Store 4
Let's prove the following theorem:
if the following are true:
- instruction #10 is
store src=3 addr=1 imm=0 - the PC at time 4 = 10
- value of cell 1 at time 4 = 127
- value of cell 3 at time 4 = 2
then value of cell 127 at time 5 = 2
Proof:
Given
| 1 | instruction #10 is store src=3 addr=1 imm=0 |
|---|---|
| 2 | the PC at time 4 = 10 |
| 3 | value of cell 1 at time 4 = 127 |
| 4 | value of cell 3 at time 4 = 2 |
| # | Claim | Reason |
|---|---|---|
| 1 | value of cell ((value of cell 1 at time 4) + 0) at time (4 + 1) = value of cell 3 at time 4 | if instruction #10 is store src=3 addr=1 imm=0 and the PC at time 4 = 10, then value of cell ((value of cell 1 at time 4) + 0) at time (4 + 1) = value of cell 3 at time 4 |
| 2 | (value of cell 1 at time 4) + 0 = 127 + 0 | if value of cell 1 at time 4 = 127, then (value of cell 1 at time 4) + 0 = 127 + 0 |
| 3 | 127 + 0 = 127 | 127 + 0 = 127 |
| 4 | (value of cell 1 at time 4) + 0 = 127 | if (value of cell 1 at time 4) + 0 = 127 + 0 and 127 + 0 = 127, then (value of cell 1 at time 4) + 0 = 127 |
| 5 | value of cell ((value of cell 1 at time 4) + 0) at time (4 + 1) = value of cell 127 at time (4 + 1) | if (value of cell 1 at time 4) + 0 = 127, then value of cell ((value of cell 1 at time 4) + 0) at time (4 + 1) = value of cell 127 at time (4 + 1) |
| 6 | 4 + 1 = 5 | 4 + 1 = 5 |
| 7 | value of cell 127 at time (4 + 1) = value of cell 127 at time 5 | if 4 + 1 = 5, then value of cell 127 at time (4 + 1) = value of cell 127 at time 5 |
| 8 | value of cell 127 at time 5 = value of cell 3 at time 4 | if value of cell ((value of cell 1 at time 4) + 0) at time (4 + 1) = value of cell 127 at time (4 + 1) and value of cell 127 at time (4 + 1) = value of cell 127 at time 5 and value of cell ((value of cell 1 at time 4) + 0) at time (4 + 1) = value of cell 3 at time 4, then value of cell 127 at time 5 = value of cell 3 at time 4 |
| 9 | value of cell 127 at time 5 = 2 | if value of cell 127 at time 5 = value of cell 3 at time 4 and value of cell 3 at time 4 = 2, then value of cell 127 at time 5 = 2 |
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