Proof: Pc 3
Let's prove the following theorem:
if the following are true:
- instruction #3 is
addi dst=5 src=5 imm=7 - the PC at time 3 = 3
then the PC at time 4 = 4
Proof:
Given
| 1 | instruction #3 is addi dst=5 src=5 imm=7 |
|---|---|
| 2 | the PC at time 3 = 3 |
| # | Claim | Reason |
|---|---|---|
| 1 | the PC at time (3 + 1) = 3 + 1 | if instruction #3 is addi dst=5 src=5 imm=7 and the PC at time 3 = 3, then the PC at time (3 + 1) = 3 + 1 |
| 2 | 3 + 1 = 4 | 3 + 1 = 4 |
| 3 | the PC at time (3 + 1) = the PC at time 4 | if 3 + 1 = 4, then the PC at time (3 + 1) = the PC at time 4 |
| 4 | the PC at time 4 = 4 | if the PC at time (3 + 1) = 3 + 1 and the PC at time (3 + 1) = the PC at time 4 and 3 + 1 = 4, then the PC at time 4 = 4 |
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