Proof: Pc 9

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 15
the PC at time 9 = 15

then the PC at time 10 = 16

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 15
2	the PC at time 9 = 15

Proof Table

#	Claim	Reason
1	the PC at time (9 + 1) = 15 + 1	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 15 and the PC at time 9 = 15, then the PC at time (9 + 1) = 15 + 1 (Program Counter on SUBTRACTI)
2	9 + 1 = 10	9 + 1 = 10 (Fixed Value Statement)
3	15 + 1 = 16	15 + 1 = 16 (Fixed Value Statement)
4	the PC at time (9 + 1) = the PC at time 10	if 9 + 1 = 10, then the PC at time (9 + 1) = the PC at time 10 (Substitution)
5	the PC at time 10 = 16	if the PC at time (9 + 1) = 15 + 1 and the PC at time (9 + 1) = the PC at time 10 and 15 + 1 = 16, then the PC at time 10 = 16 (Transitive Property Application 2)

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