Proof: Pc 11

Let's prove the following theorem:

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 11 = 4

then the PC at time 12 = 5

Proof:

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Given

1	instruction #4 is `addi dst=4 src=4 imm=1`
2	the PC at time 11 = 4

Proof Table

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

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