Proof: Byte 4 Stays the Same 5
Let's prove the following theorem:
if the following are true:
- instruction #5 is
beq left=3 right=4 imm=1
- the PC at time 5 = 5
- value of cell 4 at time 5 = 1
then value of cell 4 at time 6 = 1
Proof:
Given
1 | instruction #5 is beq left=3 right=4 imm=1 |
---|---|
2 | the PC at time 5 = 5 |
3 | value of cell 4 at time 5 = 1 |
# | Claim | Reason |
---|---|---|
1 | value of cell 4 at time (5 + 1) = value of cell 4 at time 5 | if instruction #5 is beq left=3 right=4 imm=1 and the PC at time 5 = 5, then value of cell 4 at time (5 + 1) = value of cell 4 at time 5 |
2 | 5 + 1 = 6 | 5 + 1 = 6 |
3 | value of cell 4 at time (5 + 1) = value of cell 4 at time 6 | if 5 + 1 = 6, then value of cell 4 at time (5 + 1) = value of cell 4 at time 6 |
4 | value of cell 4 at time 6 = value of cell 4 at time 5 | if value of cell 4 at time (5 + 1) = value of cell 4 at time 6 and value of cell 4 at time (5 + 1) = value of cell 4 at time 5, then value of cell 4 at time 6 = value of cell 4 at time 5 |
5 | value of cell 4 at time 6 = 1 | if value of cell 4 at time 6 = value of cell 4 at time 5 and value of cell 4 at time 5 = 1, then value of cell 4 at time 6 = 1 |
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