Proof: Pc 3

Let's prove the following theorem:

if the following are true:
  • subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 9
  • the PC at time 3 = 9

then the PC at time 4 = 10

Proof:

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Given
1 subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 9
2 the PC at time 3 = 9
Proof Table
# Claim Reason
1 the PC at time (3 + 1) = 9 + 1 if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 9 and the PC at time 3 = 9, then the PC at time (3 + 1) = 9 + 1
2 3 + 1 = 4 3 + 1 = 4
3 9 + 1 = 10 9 + 1 = 10
4 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
5 the PC at time 4 = 10 if the PC at time (3 + 1) = 9 + 1 and the PC at time (3 + 1) = the PC at time 4 and 9 + 1 = 10, then the PC at time 4 = 10

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