Proof: Store 24
Let's prove the following theorem:
if the following are true:
- instruction #24 is
store src=3 addr=1 imm=0
- the PC at time 24 = 24
- value of cell 1 at time 24 = 125
- value of cell 3 at time 24 = 5
then value of cell 125 at time 25 = 5
Proof:
Given
1 | instruction #24 is store src=3 addr=1 imm=0 |
---|---|
2 | the PC at time 24 = 24 |
3 | value of cell 1 at time 24 = 125 |
4 | value of cell 3 at time 24 = 5 |
# | Claim | Reason |
---|---|---|
1 | value of cell ((value of cell 1 at time 24) + 0) at time (24 + 1) = value of cell 3 at time 24 | if instruction #24 is store src=3 addr=1 imm=0 and the PC at time 24 = 24, then value of cell ((value of cell 1 at time 24) + 0) at time (24 + 1) = value of cell 3 at time 24 |
2 | (value of cell 1 at time 24) + 0 = 125 + 0 | if value of cell 1 at time 24 = 125, then (value of cell 1 at time 24) + 0 = 125 + 0 |
3 | 125 + 0 = 125 | 125 + 0 = 125 |
4 | (value of cell 1 at time 24) + 0 = 125 | if (value of cell 1 at time 24) + 0 = 125 + 0 and 125 + 0 = 125, then (value of cell 1 at time 24) + 0 = 125 |
5 | value of cell ((value of cell 1 at time 24) + 0) at time (24 + 1) = value of cell 125 at time (24 + 1) | if (value of cell 1 at time 24) + 0 = 125, then value of cell ((value of cell 1 at time 24) + 0) at time (24 + 1) = value of cell 125 at time (24 + 1) |
6 | 24 + 1 = 25 | 24 + 1 = 25 |
7 | value of cell 125 at time (24 + 1) = value of cell 125 at time 25 | if 24 + 1 = 25, then value of cell 125 at time (24 + 1) = value of cell 125 at time 25 |
8 | value of cell 125 at time 25 = value of cell 3 at time 24 | if value of cell ((value of cell 1 at time 24) + 0) at time (24 + 1) = value of cell 125 at time (24 + 1) and value of cell 125 at time (24 + 1) = value of cell 125 at time 25 and value of cell ((value of cell 1 at time 24) + 0) at time (24 + 1) = value of cell 3 at time 24, then value of cell 125 at time 25 = value of cell 3 at time 24 |
9 | value of cell 125 at time 25 = 5 | if value of cell 125 at time 25 = value of cell 3 at time 24 and value of cell 3 at time 24 = 5, then value of cell 125 at time 25 = 5 |
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