Proof: Byte 125 Stays the Same 14

Let's prove the following theorem:

if the following are true:

instruction #20 is a JAL instruction with jump to: 2
the PC at time 14 = 20
value of cell 125 at time 14 = 2

then value of cell 125 at time 15 = 2

Proof:

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Given

1	instruction #20 is a JAL instruction with jump to: 2
2	the PC at time 14 = 20
3	value of cell 125 at time 14 = 2

Proof Table

#	Claim	Reason
1	not (125 = 2)	not (125 = 2) (Fixed Value Statement)
2	value of cell 125 at time (14 + 1) = value of cell 125 at time 14	if instruction #20 is a JAL instruction with jump to: 2 and the PC at time 14 = 20 and not (125 = 2), then value of cell 125 at time (14 + 1) = value of cell 125 at time 14 (JAL Instruction Property 3)
3	14 + 1 = 15	14 + 1 = 15 (Fixed Value Statement)
4	value of cell 125 at time (14 + 1) = value of cell 125 at time 15	if 14 + 1 = 15, then value of cell 125 at time (14 + 1) = value of cell 125 at time 15 (Substitution)
5	value of cell 125 at time 15 = value of cell 125 at time 14	if value of cell 125 at time (14 + 1) = value of cell 125 at time 15 and value of cell 125 at time (14 + 1) = value of cell 125 at time 14, then value of cell 125 at time 15 = value of cell 125 at time 14 (Transitive Property of Equality Variation 2)
6	value of cell 125 at time 15 = 2	if value of cell 125 at time 15 = value of cell 125 at time 14 and value of cell 125 at time 14 = 2, then value of cell 125 at time 15 = 2 (Transitive Property of Equality)

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