Proof: Addi Insn 2

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 2 = 2
value of cell 5 at time 2 = 8

then value of cell 5 at time 3 = 9

Proof:

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Given

1	instruction #2 is `addi dst=5 src=5 imm=1`
2	the PC at time 2 = 2
3	value of cell 5 at time 2 = 8

Proof Table

#	Claim	Reason
1	value of cell 5 at time (2 + 1) = (value of cell 5 at time 2) + 1	if instruction #2 is `addi dst=5 src=5 imm=1` and the PC at time 2 = 2, then value of cell 5 at time (2 + 1) = (value of cell 5 at time 2) + 1 (ADDI Instruction Property)
2	2 + 1 = 3	2 + 1 = 3 (Fixed Value Statement)
3	value of cell 5 at time (2 + 1) = value of cell 5 at time 3	if 2 + 1 = 3, then value of cell 5 at time (2 + 1) = value of cell 5 at time 3 (Substitution)
4	value of cell 5 at time 3 = (value of cell 5 at time 2) + 1	if value of cell 5 at time (2 + 1) = value of cell 5 at time 3 and value of cell 5 at time (2 + 1) = (value of cell 5 at time 2) + 1, then value of cell 5 at time 3 = (value of cell 5 at time 2) + 1 (Transitive Property of Equality Variation 2)
5	value of cell 5 at time 3 = 8 + 1	if value of cell 5 at time 3 = (value of cell 5 at time 2) + 1 and value of cell 5 at time 2 = 8, then value of cell 5 at time 3 = 8 + 1 (Term 1 Substitution)
6	8 + 1 = 9	8 + 1 = 9 (Fixed Value Statement)
7	value of cell 5 at time 3 = 9	if value of cell 5 at time 3 = 8 + 1 and 8 + 1 = 9, then value of cell 5 at time 3 = 9 (Transitive Property of Equality)

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