Proof: Byte 5 Stays the Same 10

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 10 = 4
value of cell 5 at time 10 = 4

then value of cell 5 at time 11 = 4

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 10 = 4
3	value of cell 5 at time 10 = 4

Proof Table

#	Claim	Reason
1	not (5 = 3)	not (5 = 3) (Fixed Value Statement)
2	value of cell 5 at time (10 + 1) = value of cell 5 at time 10	if instruction #4 is `add dst=3 src1=1 src2=2` and the PC at time 10 = 4 and not (5 = 3), then value of cell 5 at time (10 + 1) = value of cell 5 at time 10 (ADD Instruction Property 2)
3	10 + 1 = 11	10 + 1 = 11 (Fixed Value Statement)
4	value of cell 5 at time (10 + 1) = value of cell 5 at time 11	if 10 + 1 = 11, then value of cell 5 at time (10 + 1) = value of cell 5 at time 11 (Substitution)
5	value of cell 5 at time 11 = value of cell 5 at time 10	if value of cell 5 at time (10 + 1) = value of cell 5 at time 11 and value of cell 5 at time (10 + 1) = value of cell 5 at time 10, then value of cell 5 at time 11 = value of cell 5 at time 10 (Transitive Property of Equality Variation 2)
6	value of cell 5 at time 11 = 4	if value of cell 5 at time 11 = value of cell 5 at time 10 and value of cell 5 at time 10 = 4, then value of cell 5 at time 11 = 4 (Transitive Property of Equality)

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