Proof: Addi Insn 9

Let's prove the following theorem:

if the following are true:

instruction #2 is addi dst=5 src=5 imm=1
the PC at time 9 = 2
value of cell 5 at time 9 = 9

then value of cell 5 at time 10 = 10

Proof:

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Given

1	instruction #2 is `addi dst=5 src=5 imm=1`
2	the PC at time 9 = 2
3	value of cell 5 at time 9 = 9

Proof Table

#	Claim	Reason
1	value of cell 5 at time (9 + 1) = (value of cell 5 at time 9) + 1	if instruction #2 is `addi dst=5 src=5 imm=1` and the PC at time 9 = 2, then value of cell 5 at time (9 + 1) = (value of cell 5 at time 9) + 1 (ADDI Instruction Property)
2	9 + 1 = 10	9 + 1 = 10 (Fixed Value Statement)
3	value of cell 5 at time (9 + 1) = value of cell 5 at time 10	if 9 + 1 = 10, then value of cell 5 at time (9 + 1) = value of cell 5 at time 10 (Substitution)
4	value of cell 5 at time 10 = (value of cell 5 at time 9) + 1	if value of cell 5 at time (9 + 1) = value of cell 5 at time 10 and value of cell 5 at time (9 + 1) = (value of cell 5 at time 9) + 1, then value of cell 5 at time 10 = (value of cell 5 at time 9) + 1 (Transitive Property of Equality Variation 2)
5	value of cell 5 at time 10 = 9 + 1	if value of cell 5 at time 10 = (value of cell 5 at time 9) + 1 and value of cell 5 at time 9 = 9, then value of cell 5 at time 10 = 9 + 1 (Term 1 Substitution)
6	value of cell 5 at time 10 = 10	if value of cell 5 at time 10 = 9 + 1 and 9 + 1 = 10, then value of cell 5 at time 10 = 10 (Transitive Property of Equality)

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