Proof: Byte 4 Stays the Same 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
value of cell 4 at time 22 = 3

then value of cell 4 at time 23 = 3

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
3	value of cell 4 at time 22 = 3

Proof Table

#	Claim	Reason
1	not (4 = 3)	not (4 = 3) (Fixed Value Statement)
2	value of cell 4 at time (22 + 1) = value of cell 4 at time 22	if instruction #4 is `add dst=3 src1=1 src2=2` and the PC at time 22 = 4 and not (4 = 3), then value of cell 4 at time (22 + 1) = value of cell 4 at time 22 (ADD Instruction Property 2)
3	22 + 1 = 23	22 + 1 = 23 (Fixed Value Statement)
4	value of cell 4 at time (22 + 1) = value of cell 4 at time 23	if 22 + 1 = 23, then value of cell 4 at time (22 + 1) = value of cell 4 at time 23 (Substitution)
5	value of cell 4 at time 23 = value of cell 4 at time 22	if value of cell 4 at time (22 + 1) = value of cell 4 at time 23 and value of cell 4 at time (22 + 1) = value of cell 4 at time 22, then value of cell 4 at time 23 = value of cell 4 at time 22 (Transitive Property of Equality Variation 2)
6	value of cell 4 at time 23 = 3	if value of cell 4 at time 23 = value of cell 4 at time 22 and value of cell 4 at time 22 = 3, then value of cell 4 at time 23 = 3 (Transitive Property of Equality)

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