Proof: Pc 2

Let's prove the following theorem:

if the following are true:

instruction #2 is addi dst=4 src=0 imm=0
the PC at time 2 = 2

then the PC at time 3 = 3

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #2 is `addi dst=4 src=0 imm=0`
2	the PC at time 2 = 2

Proof Table

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

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