Proof: Store 10
Let's prove the following theorem:
if the following are true:
- instruction #16 is
store src=3 addr=1 imm=0
- the PC at time 10 = 16
- value of cell 1 at time 10 = 125
- value of cell 3 at time 10 = 2
then value of cell 125 at time 11 = 2
Proof:
Given
1 | instruction #16 is store src=3 addr=1 imm=0 |
---|---|
2 | the PC at time 10 = 16 |
3 | value of cell 1 at time 10 = 125 |
4 | value of cell 3 at time 10 = 2 |
# | Claim | Reason |
---|---|---|
1 | value of cell ((value of cell 1 at time 10) + 0) at time (10 + 1) = value of cell 3 at time 10 | if instruction #16 is store src=3 addr=1 imm=0 and the PC at time 10 = 16, then value of cell ((value of cell 1 at time 10) + 0) at time (10 + 1) = value of cell 3 at time 10 |
2 | (value of cell 1 at time 10) + 0 = 125 + 0 | if value of cell 1 at time 10 = 125, then (value of cell 1 at time 10) + 0 = 125 + 0 |
3 | 125 + 0 = 125 | 125 + 0 = 125 |
4 | (value of cell 1 at time 10) + 0 = 125 | if (value of cell 1 at time 10) + 0 = 125 + 0 and 125 + 0 = 125, then (value of cell 1 at time 10) + 0 = 125 |
5 | value of cell ((value of cell 1 at time 10) + 0) at time (10 + 1) = value of cell 125 at time (10 + 1) | if (value of cell 1 at time 10) + 0 = 125, then value of cell ((value of cell 1 at time 10) + 0) at time (10 + 1) = value of cell 125 at time (10 + 1) |
6 | 10 + 1 = 11 | 10 + 1 = 11 |
7 | value of cell 125 at time (10 + 1) = value of cell 125 at time 11 | if 10 + 1 = 11, then value of cell 125 at time (10 + 1) = value of cell 125 at time 11 |
8 | value of cell 125 at time 11 = value of cell 3 at time 10 | if value of cell ((value of cell 1 at time 10) + 0) at time (10 + 1) = value of cell 125 at time (10 + 1) and value of cell 125 at time (10 + 1) = value of cell 125 at time 11 and value of cell ((value of cell 1 at time 10) + 0) at time (10 + 1) = value of cell 3 at time 10, then value of cell 125 at time 11 = value of cell 3 at time 10 |
9 | value of cell 125 at time 11 = 2 | if value of cell 125 at time 11 = value of cell 3 at time 10 and value of cell 3 at time 10 = 2, then value of cell 125 at time 11 = 2 |
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