Proof: Byte 3 Stays the Same 10

Let's prove the following theorem:

if the following are true:

instruction #6 is jump imm=3
the PC at time 10 = 6
value of cell 3 at time 10 = 3

then value of cell 3 at time 11 = 3

Proof:

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Given

1	instruction #6 is `jump imm=3`
2	the PC at time 10 = 6
3	value of cell 3 at time 10 = 3

Proof Table

#	Claim	Reason
1	value of cell 3 at time (10 + 1) = value of cell 3 at time 10	if instruction #6 is `jump imm=3` and the PC at time 10 = 6, then value of cell 3 at time (10 + 1) = value of cell 3 at time 10 (JUMP Instruction Property 2)
2	10 + 1 = 11	10 + 1 = 11 (Fixed Value Statement)
3	value of cell 3 at time (10 + 1) = value of cell 3 at time 11	if 10 + 1 = 11, then value of cell 3 at time (10 + 1) = value of cell 3 at time 11 (Substitution)
4	value of cell 3 at time 11 = value of cell 3 at time 10	if value of cell 3 at time (10 + 1) = value of cell 3 at time 11 and value of cell 3 at time (10 + 1) = value of cell 3 at time 10, then value of cell 3 at time 11 = value of cell 3 at time 10 (Transitive Property of Equality Variation 2)
5	value of cell 3 at time 11 = 3	if value of cell 3 at time 11 = value of cell 3 at time 10 and value of cell 3 at time 10 = 3, then value of cell 3 at time 11 = 3 (Transitive Property of Equality)

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