Proof: Pc 5

Let's prove the following theorem:

if the following are true:

instruction #11 is addi dst=3 src=0 imm=3
the PC at time 5 = 11

then the PC at time 6 = 12

Proof:

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Given

1	instruction #11 is `addi dst=3 src=0 imm=3`
2	the PC at time 5 = 11

Proof Table

#	Claim	Reason
1	the PC at time (5 + 1) = 11 + 1	if instruction #11 is `addi dst=3 src=0 imm=3` and the PC at time 5 = 11, then the PC at time (5 + 1) = 11 + 1 (Program Counter on ADDI)
2	5 + 1 = 6	5 + 1 = 6 (Fixed Value Statement)
3	11 + 1 = 12	11 + 1 = 12 (Fixed Value Statement)
4	the PC at time (5 + 1) = the PC at time 6	if 5 + 1 = 6, then the PC at time (5 + 1) = the PC at time 6 (Substitution)
5	the PC at time 6 = 12	if the PC at time (5 + 1) = 11 + 1 and the PC at time (5 + 1) = the PC at time 6 and 11 + 1 = 12, then the PC at time 6 = 12 (Transitive Property Application 2)

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