Proof: Addi Insn 2

Let's prove the following theorem:

if the following are true:

instruction #2 is addi dst=9 src=5 imm=0
the PC at time 2 = 2
value of cell 5 at time 2 = 20

then value of cell 9 at time 3 = 20

Proof:

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Given

1	instruction #2 is `addi dst=9 src=5 imm=0`
2	the PC at time 2 = 2
3	value of cell 5 at time 2 = 20

Proof Table

#	Claim	Reason
1	value of cell 9 at time (2 + 1) = (value of cell 5 at time 2) + 0	if instruction #2 is `addi dst=9 src=5 imm=0` and the PC at time 2 = 2, then value of cell 9 at time (2 + 1) = (value of cell 5 at time 2) + 0 (ADDI Instruction Property)
2	2 + 1 = 3	2 + 1 = 3 (Fixed Value Statement)
3	value of cell 9 at time (2 + 1) = value of cell 9 at time 3	if 2 + 1 = 3, then value of cell 9 at time (2 + 1) = value of cell 9 at time 3 (Substitution)
4	value of cell 9 at time 3 = (value of cell 5 at time 2) + 0	if value of cell 9 at time (2 + 1) = value of cell 9 at time 3 and value of cell 9 at time (2 + 1) = (value of cell 5 at time 2) + 0, then value of cell 9 at time 3 = (value of cell 5 at time 2) + 0 (Transitive Property of Equality Variation 2)
5	value of cell 9 at time 3 = 20 + 0	if value of cell 9 at time 3 = (value of cell 5 at time 2) + 0 and value of cell 5 at time 2 = 20, then value of cell 9 at time 3 = 20 + 0 (Term 1 Substitution)
6	20 + 0 = 20	20 + 0 = 20 (Additive Identity)
7	value of cell 9 at time 3 = 20	if value of cell 9 at time 3 = 20 + 0 and 20 + 0 = 20, then value of cell 9 at time 3 = 20 (Transitive Property of Equality)

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