Transitive Property of Equality Variation 2

Transitive Property Application 2

Proof: Pc 23

Let's prove the following theorem:

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 23 = 5

then the PC at time 24 = 6

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #5 is `addi dst=1 src=2 imm=0`
2	the PC at time 23 = 5

Proof Table

#	Claim	Reason
1	the PC at time (23 + 1) = 5 + 1	if instruction #5 is `addi dst=1 src=2 imm=0` and the PC at time 23 = 5, then the PC at time (23 + 1) = 5 + 1 (Program Counter on ADDI)
2	23 + 1 = 24	23 + 1 = 24 (Fixed Value Statement)
3	5 + 1 = 6	5 + 1 = 6 (Fixed Value Statement)
4	the PC at time (23 + 1) = the PC at time 24	if 23 + 1 = 24, then the PC at time (23 + 1) = the PC at time 24 (Substitution)
5	the PC at time 24 = 6	if the PC at time (23 + 1) = 5 + 1 and the PC at time (23 + 1) = the PC at time 24 and 5 + 1 = 6, then the PC at time 24 = 6 (Transitive Property Application 2)

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