Proof: Byte 2 Stays the Same 23

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 23
the PC at time 23 = 23
value of cell 2 at time 23 = 21

then value of cell 2 at time 24 = 21

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 23
2	the PC at time 23 = 23
3	value of cell 2 at time 23 = 21

Proof Table

#	Claim	Reason
1	not (2 = 1)	not (2 = 1) (Fixed Value Statement)
2	value of cell 2 at time (23 + 1) = value of cell 2 at time 23	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 23 and the PC at time 23 = 23 and not (2 = 1), then value of cell 2 at time (23 + 1) = value of cell 2 at time 23 (SUBTRACTI Instruction, Others)
3	23 + 1 = 24	23 + 1 = 24 (Fixed Value Statement)
4	value of cell 2 at time (23 + 1) = value of cell 2 at time 24	if 23 + 1 = 24, then value of cell 2 at time (23 + 1) = value of cell 2 at time 24 (Substitution)
5	value of cell 2 at time 24 = value of cell 2 at time 23	if value of cell 2 at time (23 + 1) = value of cell 2 at time 24 and value of cell 2 at time (23 + 1) = value of cell 2 at time 23, then value of cell 2 at time 24 = value of cell 2 at time 23 (Transitive Property of Equality Variation 2)
6	value of cell 2 at time 24 = 21	if value of cell 2 at time 24 = value of cell 2 at time 23 and value of cell 2 at time 23 = 21, then value of cell 2 at time 24 = 21 (Transitive Property of Equality)

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