Proof: Byte 2 Stays the Same 15

Let's prove the following theorem:

if the following are true:

instruction #9 is jump imm=(-6)
the PC at time 15 = 9
value of cell 2 at time 15 = 2

then value of cell 2 at time 16 = 2

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #9 is `jump imm=(-6)`
2	the PC at time 15 = 9
3	value of cell 2 at time 15 = 2

Proof Table

#	Claim	Reason
1	value of cell 2 at time (15 + 1) = value of cell 2 at time 15	if instruction #9 is `jump imm=(-6)` and the PC at time 15 = 9, then value of cell 2 at time (15 + 1) = value of cell 2 at time 15 (JUMP Instruction Property 2)
2	15 + 1 = 16	15 + 1 = 16 (Fixed Value Statement)
3	value of cell 2 at time (15 + 1) = value of cell 2 at time 16	if 15 + 1 = 16, then value of cell 2 at time (15 + 1) = value of cell 2 at time 16 (Substitution)
4	value of cell 2 at time 16 = value of cell 2 at time 15	if value of cell 2 at time (15 + 1) = value of cell 2 at time 16 and value of cell 2 at time (15 + 1) = value of cell 2 at time 15, then value of cell 2 at time 16 = value of cell 2 at time 15 (Transitive Property of Equality Variation 2)
5	value of cell 2 at time 16 = 2	if value of cell 2 at time 16 = value of cell 2 at time 15 and value of cell 2 at time 15 = 2, then value of cell 2 at time 16 = 2 (Transitive Property of Equality)

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