Proof: Byte 5 Stays the Same 12

Let's prove the following theorem:

if the following are true:

instruction #4 is addi dst=4 src=4 imm=1
the PC at time 12 = 4
value of cell 5 at time 12 = 21

then value of cell 5 at time 13 = 21

Proof:

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Given

1	instruction #4 is `addi dst=4 src=4 imm=1`
2	the PC at time 12 = 4
3	value of cell 5 at time 12 = 21

Proof Table

#	Claim	Reason
1	not (5 = 4)	not (5 = 4) (Fixed Value Statement)
2	value of cell 5 at time (12 + 1) = value of cell 5 at time 12	if instruction #4 is `addi dst=4 src=4 imm=1` and the PC at time 12 = 4 and not (5 = 4), then value of cell 5 at time (12 + 1) = value of cell 5 at time 12 (ADDI Instruction Property 2)
3	12 + 1 = 13	12 + 1 = 13 (Fixed Value Statement)
4	value of cell 5 at time (12 + 1) = value of cell 5 at time 13	if 12 + 1 = 13, then value of cell 5 at time (12 + 1) = value of cell 5 at time 13 (Substitution)
5	value of cell 5 at time 13 = value of cell 5 at time 12	if value of cell 5 at time (12 + 1) = value of cell 5 at time 13 and value of cell 5 at time (12 + 1) = value of cell 5 at time 12, then value of cell 5 at time 13 = value of cell 5 at time 12 (Transitive Property of Equality Variation 2)
6	value of cell 5 at time 13 = 21	if value of cell 5 at time 13 = value of cell 5 at time 12 and value of cell 5 at time 12 = 21, then value of cell 5 at time 13 = 21 (Transitive Property of Equality)

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