Proof: Byte 3 Stays the Same 21

Let's prove the following theorem:

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 21 = 9
value of cell 3 at time 21 = 3

then value of cell 3 at time 22 = 3

Instructions

jump imm=4

Memory Cells
0
1
2
3

Program Counter	Time
9	21

LW Computer Simulator

Proof:

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Given

1	instruction #9 is `jump imm=(-6)`
2	the PC at time 21 = 9
3	value of cell 3 at time 21 = 3

Proof Table

#	Claim	Reason
1	value of cell 3 at time (21 + 1) = value of cell 3 at time 21	if instruction #9 is `jump imm=(-6)` and the PC at time 21 = 9, then value of cell 3 at time (21 + 1) = value of cell 3 at time 21 (JUMP Instruction Property 2)
2	21 + 1 = 22	21 + 1 = 22 (Fixed Value Statement)
3	value of cell 3 at time (21 + 1) = value of cell 3 at time 22	if 21 + 1 = 22, then value of cell 3 at time (21 + 1) = value of cell 3 at time 22 (Substitution)
4	value of cell 3 at time 22 = value of cell 3 at time 21	if value of cell 3 at time (21 + 1) = value of cell 3 at time 22 and value of cell 3 at time (21 + 1) = value of cell 3 at time 21, then value of cell 3 at time 22 = value of cell 3 at time 21 (Transitive Property of Equality Variation 2)
5	value of cell 3 at time 22 = 3	if value of cell 3 at time 22 = value of cell 3 at time 21 and value of cell 3 at time 21 = 3, then value of cell 3 at time 22 = 3 (Transitive Property of Equality)

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