Proof: Pc 18

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 5
the PC at time 18 = 5

then the PC at time 19 = 6

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 5
2	the PC at time 18 = 5

Proof Table

#	Claim	Reason
1	the PC at time (18 + 1) = 5 + 1	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 5 and the PC at time 18 = 5, then the PC at time (18 + 1) = 5 + 1 (Program Counter on SUBTRACTI)
2	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
3	5 + 1 = 6	5 + 1 = 6 (Fixed Value Statement)
4	the PC at time (18 + 1) = the PC at time 19	if 18 + 1 = 19, then the PC at time (18 + 1) = the PC at time 19 (Substitution)
5	the PC at time 19 = 6	if the PC at time (18 + 1) = 5 + 1 and the PC at time (18 + 1) = the PC at time 19 and 5 + 1 = 6, then the PC at time 19 = 6 (Transitive Property Application 2)

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