Proof: Byte 125 Stays the Same 12

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 18
the PC at time 12 = 18
value of cell 125 at time 12 = 2

then value of cell 125 at time 13 = 2

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 18
2	the PC at time 12 = 18
3	value of cell 125 at time 12 = 2

Proof Table

#	Claim	Reason
1	not (125 = 1)	not (125 = 1) (Fixed Value Statement)
2	value of cell 125 at time (12 + 1) = value of cell 125 at time 12	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 18 and the PC at time 12 = 18 and not (125 = 1), then value of cell 125 at time (12 + 1) = value of cell 125 at time 12 (SUBTRACTI Instruction, Others)
3	12 + 1 = 13	12 + 1 = 13 (Fixed Value Statement)
4	value of cell 125 at time (12 + 1) = value of cell 125 at time 13	if 12 + 1 = 13, then value of cell 125 at time (12 + 1) = value of cell 125 at time 13 (Substitution)
5	value of cell 125 at time 13 = value of cell 125 at time 12	if value of cell 125 at time (12 + 1) = value of cell 125 at time 13 and value of cell 125 at time (12 + 1) = value of cell 125 at time 12, then value of cell 125 at time 13 = value of cell 125 at time 12 (Transitive Property of Equality Variation 2)
6	value of cell 125 at time 13 = 2	if value of cell 125 at time 13 = value of cell 125 at time 12 and value of cell 125 at time 12 = 2, then value of cell 125 at time 13 = 2 (Transitive Property of Equality)

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