Proof: Byte 1 Stays the Same 16

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 16 = 4
value of cell 1 at time 16 = 1

then value of cell 1 at time 17 = 1

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 16 = 4
3	value of cell 1 at time 16 = 1

Proof Table

#	Claim	Reason
1	not (1 = 3)	not (1 = 3) (Fixed Value Statement)
2	value of cell 1 at time (16 + 1) = value of cell 1 at time 16	if instruction #4 is `add dst=3 src1=1 src2=2` and the PC at time 16 = 4 and not (1 = 3), then value of cell 1 at time (16 + 1) = value of cell 1 at time 16 (ADD Instruction Property 2)
3	16 + 1 = 17	16 + 1 = 17 (Fixed Value Statement)
4	value of cell 1 at time (16 + 1) = value of cell 1 at time 17	if 16 + 1 = 17, then value of cell 1 at time (16 + 1) = value of cell 1 at time 17 (Substitution)
5	value of cell 1 at time 17 = value of cell 1 at time 16	if value of cell 1 at time (16 + 1) = value of cell 1 at time 17 and value of cell 1 at time (16 + 1) = value of cell 1 at time 16, then value of cell 1 at time 17 = value of cell 1 at time 16 (Transitive Property of Equality Variation 2)
6	value of cell 1 at time 17 = 1	if value of cell 1 at time 17 = value of cell 1 at time 16 and value of cell 1 at time 16 = 1, then value of cell 1 at time 17 = 1 (Transitive Property of Equality)

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