Proof: Byte 3 Stays the Same 18

Let's prove the following theorem:

if the following are true:

subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 5
the PC at time 18 = 5
value of cell 3 at time 18 = 5

then value of cell 3 at time 19 = 5

Proof:

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Given

1	subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 5
2	the PC at time 18 = 5
3	value of cell 3 at time 18 = 5

Proof Table

#	Claim	Reason
1	not (3 = 1)	not (3 = 1) (Fixed Value Statement)
2	value of cell 3 at time (18 + 1) = value of cell 3 at time 18	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 5 and the PC at time 18 = 5 and not (3 = 1), then value of cell 3 at time (18 + 1) = value of cell 3 at time 18 (SUBTRACTI Instruction, Others)
3	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
4	value of cell 3 at time (18 + 1) = value of cell 3 at time 19	if 18 + 1 = 19, then value of cell 3 at time (18 + 1) = value of cell 3 at time 19 (Substitution)
5	value of cell 3 at time 19 = value of cell 3 at time 18	if value of cell 3 at time (18 + 1) = value of cell 3 at time 19 and value of cell 3 at time (18 + 1) = value of cell 3 at time 18, then value of cell 3 at time 19 = value of cell 3 at time 18 (Transitive Property of Equality Variation 2)
6	value of cell 3 at time 19 = 5	if value of cell 3 at time 19 = value of cell 3 at time 18 and value of cell 3 at time 18 = 5, then value of cell 3 at time 19 = 5 (Transitive Property of Equality)

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