Proof: Pc 23

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 23
the PC at time 23 = 23

then the PC at time 24 = 24

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 23
2	the PC at time 23 = 23

Proof Table

#	Claim	Reason
1	the PC at time (23 + 1) = 23 + 1	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 23 and the PC at time 23 = 23, then the PC at time (23 + 1) = 23 + 1 (Program Counter on SUBTRACTI)
2	23 + 1 = 24	23 + 1 = 24 (Fixed Value Statement)
3	the PC at time (23 + 1) = the PC at time 24	if 23 + 1 = 24, then the PC at time (23 + 1) = the PC at time 24 (Substitution)
4	the PC at time 24 = 24	if the PC at time (23 + 1) = 23 + 1 and the PC at time (23 + 1) = the PC at time 24 and 23 + 1 = 24, then the PC at time 24 = 24 (Transitive Property Application 2)

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