Proof: Load 1
Let's prove the following theorem:
if the following are true:
- instruction #1 is
load dst=8 addr=6 imm=1 - the PC at time 1 = 1
- value of cell 6 at time 1 = 3
- value of cell 4 at time 1 = 11
then value of cell 8 at time 2 = 11
Proof:
Given
| 1 | instruction #1 is load dst=8 addr=6 imm=1 |
|---|---|
| 2 | the PC at time 1 = 1 |
| 3 | value of cell 6 at time 1 = 3 |
| 4 | value of cell 4 at time 1 = 11 |
| # | Claim | Reason |
|---|---|---|
| 1 | value of cell 8 at time (1 + 1) = value of cell ((value of cell 6 at time 1) + 1) at time 1 | if instruction #1 is load dst=8 addr=6 imm=1 and the PC at time 1 = 1, then value of cell 8 at time (1 + 1) = value of cell ((value of cell 6 at time 1) + 1) at time 1 |
| 2 | (value of cell 6 at time 1) + 1 = 3 + 1 | if value of cell 6 at time 1 = 3, then (value of cell 6 at time 1) + 1 = 3 + 1 |
| 3 | 3 + 1 = 4 | 3 + 1 = 4 |
| 4 | (value of cell 6 at time 1) + 1 = 4 | if (value of cell 6 at time 1) + 1 = 3 + 1 and 3 + 1 = 4, then (value of cell 6 at time 1) + 1 = 4 |
| 5 | value of cell ((value of cell 6 at time 1) + 1) at time 1 = value of cell 4 at time 1 | if (value of cell 6 at time 1) + 1 = 4, then value of cell ((value of cell 6 at time 1) + 1) at time 1 = value of cell 4 at time 1 |
| 6 | value of cell ((value of cell 6 at time 1) + 1) at time 1 = 11 | if value of cell ((value of cell 6 at time 1) + 1) at time 1 = value of cell 4 at time 1 and value of cell 4 at time 1 = 11, then value of cell ((value of cell 6 at time 1) + 1) at time 1 = 11 |
| 7 | value of cell 8 at time (1 + 1) = 11 | if value of cell 8 at time (1 + 1) = value of cell ((value of cell 6 at time 1) + 1) at time 1 and value of cell ((value of cell 6 at time 1) + 1) at time 1 = 11, then value of cell 8 at time (1 + 1) = 11 |
| 8 | 1 + 1 = 2 | 1 + 1 = 2 |
| 9 | value of cell 8 at time (1 + 1) = value of cell 8 at time 2 | if 1 + 1 = 2, then value of cell 8 at time (1 + 1) = value of cell 8 at time 2 |
| 10 | value of cell 8 at time 2 = 11 | if value of cell 8 at time (1 + 1) = value of cell 8 at time 2 and value of cell 8 at time (1 + 1) = 11, then value of cell 8 at time 2 = 11 |
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