Proof: Subtracti Insn 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 1 at time 9 = 126

then value of cell 1 at time 10 = 125

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 1 at time 9 = 126

Proof Table

#	Claim	Reason
1	value of cell 1 at time (9 + 1) = (value of cell 1 at time 9) - 1	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 15 and the PC at time 9 = 15, then value of cell 1 at time (9 + 1) = (value of cell 1 at time 9) - 1 (SUBTRACTI Instruction)
2	9 + 1 = 10	9 + 1 = 10 (Fixed Value Statement)
3	value of cell 1 at time (9 + 1) = value of cell 1 at time 10	if 9 + 1 = 10, then value of cell 1 at time (9 + 1) = value of cell 1 at time 10 (Substitution)
4	value of cell 1 at time 10 = (value of cell 1 at time 9) - 1	if value of cell 1 at time (9 + 1) = value of cell 1 at time 10 and value of cell 1 at time (9 + 1) = (value of cell 1 at time 9) - 1, then value of cell 1 at time 10 = (value of cell 1 at time 9) - 1 (Transitive Property of Equality Variation 2)
5	(value of cell 1 at time 9) - 1 = 126 - 1	if value of cell 1 at time 9 = 126, then (value of cell 1 at time 9) - 1 = 126 - 1 (Subtract From Both Sides Mirror)
6	value of cell 1 at time 10 = 126 - 1	if value of cell 1 at time 10 = (value of cell 1 at time 9) - 1 and (value of cell 1 at time 9) - 1 = 126 - 1, then value of cell 1 at time 10 = 126 - 1 (Transitive Property of Equality)
7	126 - 1 = 125	126 - 1 = 125 (Fixed Value Statement)
8	value of cell 1 at time 10 = 125	if value of cell 1 at time 10 = 126 - 1 and 126 - 1 = 125, then value of cell 1 at time 10 = 125 (Transitive Property of Equality)

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