Proof: Pc 2

Let's prove the following theorem:

if the following are true:

instruction #8 is addi dst=3 src=0 imm=2
the PC at time 2 = 8

then the PC at time 3 = 9

Proof:

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Given

1	instruction #8 is `addi dst=3 src=0 imm=2`
2	the PC at time 2 = 8

Proof Table

#	Claim	Reason
1	the PC at time (2 + 1) = 8 + 1	if instruction #8 is `addi dst=3 src=0 imm=2` and the PC at time 2 = 8, then the PC at time (2 + 1) = 8 + 1 (Program Counter on ADDI)
2	2 + 1 = 3	2 + 1 = 3 (Fixed Value Statement)
3	8 + 1 = 9	8 + 1 = 9 (Fixed Value Statement)
4	the PC at time (2 + 1) = the PC at time 3	if 2 + 1 = 3, then the PC at time (2 + 1) = the PC at time 3 (Substitution)
5	the PC at time 3 = 9	if the PC at time (2 + 1) = 8 + 1 and the PC at time (2 + 1) = the PC at time 3 and 8 + 1 = 9, then the PC at time 3 = 9 (Transitive Property Application 2)

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