Proof: Byte 123 Stays the Same 22

Let's prove the following theorem:

if the following are true:

instruction #22 is addi dst=1 src=1 imm=3
the PC at time 22 = 22
value of cell 123 at time 22 = 5

then value of cell 123 at time 23 = 5

Proof:

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Given

1	instruction #22 is `addi dst=1 src=1 imm=3`
2	the PC at time 22 = 22
3	value of cell 123 at time 22 = 5

Proof Table

#	Claim	Reason
1	not (123 = 1)	not (123 = 1) (Fixed Value Statement)
2	value of cell 123 at time (22 + 1) = value of cell 123 at time 22	if instruction #22 is `addi dst=1 src=1 imm=3` and the PC at time 22 = 22 and not (123 = 1), then value of cell 123 at time (22 + 1) = value of cell 123 at time 22 (ADDI Instruction Property 2)
3	22 + 1 = 23	22 + 1 = 23 (Fixed Value Statement)
4	value of cell 123 at time (22 + 1) = value of cell 123 at time 23	if 22 + 1 = 23, then value of cell 123 at time (22 + 1) = value of cell 123 at time 23 (Substitution)
5	value of cell 123 at time 23 = value of cell 123 at time 22	if value of cell 123 at time (22 + 1) = value of cell 123 at time 23 and value of cell 123 at time (22 + 1) = value of cell 123 at time 22, then value of cell 123 at time 23 = value of cell 123 at time 22 (Transitive Property of Equality Variation 2)
6	value of cell 123 at time 23 = 5	if value of cell 123 at time 23 = value of cell 123 at time 22 and value of cell 123 at time 22 = 5, then value of cell 123 at time 23 = 5 (Transitive Property of Equality)

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