Proof: Byte 3 Stays the Same 7

Let's prove the following theorem:

if the following are true:

instruction #3 is addi dst=5 src=5 imm=7
the PC at time 7 = 3
value of cell 3 at time 7 = 3

then value of cell 3 at time 8 = 3

Proof:

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Given

1	instruction #3 is `addi dst=5 src=5 imm=7`
2	the PC at time 7 = 3
3	value of cell 3 at time 7 = 3

Proof Table

#	Claim	Reason
1	not (3 = 5)	not (3 = 5) (Fixed Value Statement)
2	value of cell 3 at time (7 + 1) = value of cell 3 at time 7	if instruction #3 is `addi dst=5 src=5 imm=7` and the PC at time 7 = 3 and not (3 = 5), then value of cell 3 at time (7 + 1) = value of cell 3 at time 7 (ADDI Instruction Property 2)
3	7 + 1 = 8	7 + 1 = 8 (Fixed Value Statement)
4	value of cell 3 at time (7 + 1) = value of cell 3 at time 8	if 7 + 1 = 8, then value of cell 3 at time (7 + 1) = value of cell 3 at time 8 (Substitution)
5	value of cell 3 at time 8 = value of cell 3 at time 7	if value of cell 3 at time (7 + 1) = value of cell 3 at time 8 and value of cell 3 at time (7 + 1) = value of cell 3 at time 7, then value of cell 3 at time 8 = value of cell 3 at time 7 (Transitive Property of Equality Variation 2)
6	value of cell 3 at time 8 = 3	if value of cell 3 at time 8 = value of cell 3 at time 7 and value of cell 3 at time 7 = 3, then value of cell 3 at time 8 = 3 (Transitive Property of Equality)

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