Proof: Pc 6

Let's prove the following theorem:

if the following are true:
  • subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 12
  • the PC at time 6 = 12

then the PC at time 7 = 13

Proof:

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Given
1 subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 12
2 the PC at time 6 = 12
Proof Table
# Claim Reason
1 the PC at time (6 + 1) = 12 + 1 if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 12 and the PC at time 6 = 12, then the PC at time (6 + 1) = 12 + 1
2 6 + 1 = 7 6 + 1 = 7
3 12 + 1 = 13 12 + 1 = 13
4 the PC at time (6 + 1) = the PC at time 7 if 6 + 1 = 7, then the PC at time (6 + 1) = the PC at time 7
5 the PC at time 7 = 13 if the PC at time (6 + 1) = 12 + 1 and the PC at time (6 + 1) = the PC at time 7 and 12 + 1 = 13, then the PC at time 7 = 13

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