Proof: Byte 127 Stays the Same 9

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 15
the PC at time 9 = 15
value of cell 127 at time 9 = 2

then value of cell 127 at time 10 = 2

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 15
2	the PC at time 9 = 15
3	value of cell 127 at time 9 = 2

Proof Table

#	Claim	Reason
1	not (127 = 1)	not (127 = 1) (Fixed Value Statement)
2	value of cell 127 at time (9 + 1) = value of cell 127 at time 9	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 15 and the PC at time 9 = 15 and not (127 = 1), then value of cell 127 at time (9 + 1) = value of cell 127 at time 9 (SUBTRACTI Instruction, Others)
3	9 + 1 = 10	9 + 1 = 10 (Fixed Value Statement)
4	value of cell 127 at time (9 + 1) = value of cell 127 at time 10	if 9 + 1 = 10, then value of cell 127 at time (9 + 1) = value of cell 127 at time 10 (Substitution)
5	value of cell 127 at time 10 = value of cell 127 at time 9	if value of cell 127 at time (9 + 1) = value of cell 127 at time 10 and value of cell 127 at time (9 + 1) = value of cell 127 at time 9, then value of cell 127 at time 10 = value of cell 127 at time 9 (Transitive Property of Equality Variation 2)
6	value of cell 127 at time 10 = 2	if value of cell 127 at time 10 = value of cell 127 at time 9 and value of cell 127 at time 9 = 2, then value of cell 127 at time 10 = 2 (Transitive Property of Equality)

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