Proof: Subtracti Insn 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 1 at time 18 = 124

then value of cell 1 at time 19 = 123

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 1 at time 18 = 124

Proof Table

#	Claim	Reason
1	value of cell 1 at time (18 + 1) = (value of cell 1 at time 18) - 1	if subtract immediate instruction with dst: 1 src: 1 and immediate: 1 at 5 and the PC at time 18 = 5, then value of cell 1 at time (18 + 1) = (value of cell 1 at time 18) - 1 (SUBTRACTI Instruction)
2	18 + 1 = 19	18 + 1 = 19 (Fixed Value Statement)
3	value of cell 1 at time (18 + 1) = value of cell 1 at time 19	if 18 + 1 = 19, then value of cell 1 at time (18 + 1) = value of cell 1 at time 19 (Substitution)
4	value of cell 1 at time 19 = (value of cell 1 at time 18) - 1	if value of cell 1 at time (18 + 1) = value of cell 1 at time 19 and value of cell 1 at time (18 + 1) = (value of cell 1 at time 18) - 1, then value of cell 1 at time 19 = (value of cell 1 at time 18) - 1 (Transitive Property of Equality Variation 2)
5	(value of cell 1 at time 18) - 1 = 124 - 1	if value of cell 1 at time 18 = 124, then (value of cell 1 at time 18) - 1 = 124 - 1 (Subtract From Both Sides Mirror)
6	value of cell 1 at time 19 = 124 - 1	if value of cell 1 at time 19 = (value of cell 1 at time 18) - 1 and (value of cell 1 at time 18) - 1 = 124 - 1, then value of cell 1 at time 19 = 124 - 1 (Transitive Property of Equality)
7	124 - 1 = 123	124 - 1 = 123 (Fixed Value Statement)
8	value of cell 1 at time 19 = 123	if value of cell 1 at time 19 = 124 - 1 and 124 - 1 = 123, then value of cell 1 at time 19 = 123 (Transitive Property of Equality)

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