Proof: Byte 5 Stays the Same 23

Let's prove the following theorem:

if the following are true:

instruction #5 is addi dst=1 src=2 imm=0
the PC at time 23 = 5
value of cell 5 at time 23 = 4

then value of cell 5 at time 24 = 4

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #5 is `addi dst=1 src=2 imm=0`
2	the PC at time 23 = 5
3	value of cell 5 at time 23 = 4

Proof Table

#	Claim	Reason
1	not (5 = 1)	not (5 = 1) (Fixed Value Statement)
2	value of cell 5 at time (23 + 1) = value of cell 5 at time 23	if instruction #5 is `addi dst=1 src=2 imm=0` and the PC at time 23 = 5 and not (5 = 1), then value of cell 5 at time (23 + 1) = value of cell 5 at time 23 (ADDI Instruction Property 2)
3	23 + 1 = 24	23 + 1 = 24 (Fixed Value Statement)
4	value of cell 5 at time (23 + 1) = value of cell 5 at time 24	if 23 + 1 = 24, then value of cell 5 at time (23 + 1) = value of cell 5 at time 24 (Substitution)
5	value of cell 5 at time 24 = value of cell 5 at time 23	if value of cell 5 at time (23 + 1) = value of cell 5 at time 24 and value of cell 5 at time (23 + 1) = value of cell 5 at time 23, then value of cell 5 at time 24 = value of cell 5 at time 23 (Transitive Property of Equality Variation 2)
6	value of cell 5 at time 24 = 4	if value of cell 5 at time 24 = value of cell 5 at time 23 and value of cell 5 at time 23 = 4, then value of cell 5 at time 24 = 4 (Transitive Property of Equality)

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