Transitive Property of Equality Variation 2

Transitive Property Application 2

Proof: Pc 22

Let's prove the following theorem:

if the following are true:

instruction #4 is add dst=3 src1=1 src2=2
the PC at time 22 = 4

then the PC at time 23 = 5

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #4 is `add dst=3 src1=1 src2=2`
2	the PC at time 22 = 4

Proof Table

#	Claim	Reason
1	the PC at time (22 + 1) = 4 + 1	if instruction #4 is `add dst=3 src1=1 src2=2` and the PC at time 22 = 4, then the PC at time (22 + 1) = 4 + 1 (Program Counter on ADD)
2	22 + 1 = 23	22 + 1 = 23 (Fixed Value Statement)
3	4 + 1 = 5	4 + 1 = 5 (Fixed Value Statement)
4	the PC at time (22 + 1) = the PC at time 23	if 22 + 1 = 23, then the PC at time (22 + 1) = the PC at time 23 (Substitution)
5	the PC at time 23 = 5	if the PC at time (22 + 1) = 4 + 1 and the PC at time (22 + 1) = the PC at time 23 and 4 + 1 = 5, then the PC at time 23 = 5 (Transitive Property Application 2)

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