Proof: Store 1
Let's prove the following theorem:
if the following are true:
- instruction #1 is
store src=7 addr=6 imm=0
- the PC at time 1 = 1
- value of cell 6 at time 1 = 12
- value of cell 7 at time 1 = 24
then value of cell 12 at time 2 = 24
Proof:
Given
1 | instruction #1 is store src=7 addr=6 imm=0 |
---|---|
2 | the PC at time 1 = 1 |
3 | value of cell 6 at time 1 = 12 |
4 | value of cell 7 at time 1 = 24 |
# | Claim | Reason |
---|---|---|
1 | value of cell ((value of cell 6 at time 1) + 0) at time (1 + 1) = value of cell 7 at time 1 | if instruction #1 is store src=7 addr=6 imm=0 and the PC at time 1 = 1, then value of cell ((value of cell 6 at time 1) + 0) at time (1 + 1) = value of cell 7 at time 1 |
2 | (value of cell 6 at time 1) + 0 = 12 + 0 | if value of cell 6 at time 1 = 12, then (value of cell 6 at time 1) + 0 = 12 + 0 |
3 | 12 + 0 = 12 | 12 + 0 = 12 |
4 | (value of cell 6 at time 1) + 0 = 12 | if (value of cell 6 at time 1) + 0 = 12 + 0 and 12 + 0 = 12, then (value of cell 6 at time 1) + 0 = 12 |
5 | value of cell ((value of cell 6 at time 1) + 0) at time (1 + 1) = value of cell 12 at time (1 + 1) | if (value of cell 6 at time 1) + 0 = 12, then value of cell ((value of cell 6 at time 1) + 0) at time (1 + 1) = value of cell 12 at time (1 + 1) |
6 | 1 + 1 = 2 | 1 + 1 = 2 |
7 | value of cell 12 at time (1 + 1) = value of cell 12 at time 2 | if 1 + 1 = 2, then value of cell 12 at time (1 + 1) = value of cell 12 at time 2 |
8 | value of cell 12 at time 2 = value of cell 7 at time 1 | if value of cell ((value of cell 6 at time 1) + 0) at time (1 + 1) = value of cell 12 at time (1 + 1) and value of cell 12 at time (1 + 1) = value of cell 12 at time 2 and value of cell ((value of cell 6 at time 1) + 0) at time (1 + 1) = value of cell 7 at time 1, then value of cell 12 at time 2 = value of cell 7 at time 1 |
9 | value of cell 12 at time 2 = 24 | if value of cell 12 at time 2 = value of cell 7 at time 1 and value of cell 7 at time 1 = 24, then value of cell 12 at time 2 = 24 |
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