Proof: Byte 3 Stays the Same 4

Let's prove the following theorem:

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 4 = 4
value of cell 3 at time 4 = 3

then value of cell 3 at time 5 = 3

Proof:

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Given

1	instruction #4 is `addi dst=4 src=4 imm=1`
2	the PC at time 4 = 4
3	value of cell 3 at time 4 = 3

Proof Table

#	Claim	Reason
1	not (3 = 4)	not (3 = 4) (Fixed Value Statement)
2	value of cell 3 at time (4 + 1) = value of cell 3 at time 4	if instruction #4 is `addi dst=4 src=4 imm=1` and the PC at time 4 = 4 and not (3 = 4), then value of cell 3 at time (4 + 1) = value of cell 3 at time 4 (ADDI Instruction Property 2)
3	4 + 1 = 5	4 + 1 = 5 (Fixed Value Statement)
4	value of cell 3 at time (4 + 1) = value of cell 3 at time 5	if 4 + 1 = 5, then value of cell 3 at time (4 + 1) = value of cell 3 at time 5 (Substitution)
5	value of cell 3 at time 5 = value of cell 3 at time 4	if value of cell 3 at time (4 + 1) = value of cell 3 at time 5 and value of cell 3 at time (4 + 1) = value of cell 3 at time 4, then value of cell 3 at time 5 = value of cell 3 at time 4 (Transitive Property of Equality Variation 2)
6	value of cell 3 at time 5 = 3	if value of cell 3 at time 5 = value of cell 3 at time 4 and value of cell 3 at time 4 = 3, then value of cell 3 at time 5 = 3 (Transitive Property of Equality)

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