Proof: Addi Insn 3

Let's prove the following theorem:

if the following are true:

instruction #3 is addi dst=6 src=6 imm=1
the PC at time 3 = 3
value of cell 6 at time 3 = 12

then value of cell 6 at time 4 = 13

Proof:

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Given

1	instruction #3 is `addi dst=6 src=6 imm=1`
2	the PC at time 3 = 3
3	value of cell 6 at time 3 = 12

Proof Table

#	Claim	Reason
1	value of cell 6 at time (3 + 1) = (value of cell 6 at time 3) + 1	if instruction #3 is `addi dst=6 src=6 imm=1` and the PC at time 3 = 3, then value of cell 6 at time (3 + 1) = (value of cell 6 at time 3) + 1 (ADDI Instruction Property)
2	3 + 1 = 4	3 + 1 = 4 (Fixed Value Statement)
3	value of cell 6 at time (3 + 1) = value of cell 6 at time 4	if 3 + 1 = 4, then value of cell 6 at time (3 + 1) = value of cell 6 at time 4 (Substitution)
4	value of cell 6 at time 4 = (value of cell 6 at time 3) + 1	if value of cell 6 at time (3 + 1) = value of cell 6 at time 4 and value of cell 6 at time (3 + 1) = (value of cell 6 at time 3) + 1, then value of cell 6 at time 4 = (value of cell 6 at time 3) + 1 (Transitive Property of Equality Variation 2)
5	value of cell 6 at time 4 = 12 + 1	if value of cell 6 at time 4 = (value of cell 6 at time 3) + 1 and value of cell 6 at time 3 = 12, then value of cell 6 at time 4 = 12 + 1 (Term 1 Substitution)
6	12 + 1 = 13	12 + 1 = 13 (Fixed Value Statement)
7	value of cell 6 at time 4 = 13	if value of cell 6 at time 4 = 12 + 1 and 12 + 1 = 13, then value of cell 6 at time 4 = 13 (Transitive Property of Equality)

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