Proof: Pc 12

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 18
the PC at time 12 = 18

then the PC at time 13 = 19

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 18
2	the PC at time 12 = 18

Proof Table

#	Claim	Reason
1	the PC at time (12 + 1) = 18 + 1	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 18 and the PC at time 12 = 18, then the PC at time (12 + 1) = 18 + 1 (Program Counter on SUBTRACTI)
2	12 + 1 = 13	12 + 1 = 13 (Fixed Value Statement)
3	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
4	the PC at time (12 + 1) = the PC at time 13	if 12 + 1 = 13, then the PC at time (12 + 1) = the PC at time 13 (Substitution)
5	the PC at time 13 = 19	if the PC at time (12 + 1) = 18 + 1 and the PC at time (12 + 1) = the PC at time 13 and 18 + 1 = 19, then the PC at time 13 = 19 (Transitive Property Application 2)

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