Proof: Pc 17

Let's prove the following theorem:

if the following are true:

instruction #4 is add dst=3 src1=3 src2=4
the PC at time 17 = 4

then the PC at time 18 = 5

Proof:

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Given

1	instruction #4 is `add dst=3 src1=3 src2=4`
2	the PC at time 17 = 4

Proof Table

#	Claim	Reason
1	the PC at time (17 + 1) = 4 + 1	if instruction #4 is `add dst=3 src1=3 src2=4` and the PC at time 17 = 4, then the PC at time (17 + 1) = 4 + 1 (Program Counter on ADD)
2	17 + 1 = 18	17 + 1 = 18 (Fixed Value Statement)
3	4 + 1 = 5	4 + 1 = 5 (Fixed Value Statement)
4	the PC at time (17 + 1) = the PC at time 18	if 17 + 1 = 18, then the PC at time (17 + 1) = the PC at time 18 (Substitution)
5	the PC at time 18 = 5	if the PC at time (17 + 1) = 4 + 1 and the PC at time (17 + 1) = the PC at time 18 and 4 + 1 = 5, then the PC at time 18 = 5 (Transitive Property Application 2)

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