Proof: Byte 4 Stays the Same 24

Let's prove the following theorem:

if the following are true:

instruction #6 is addi dst=2 src=3 imm=0
the PC at time 24 = 6
value of cell 4 at time 24 = 3

then value of cell 4 at time 25 = 3

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #6 is `addi dst=2 src=3 imm=0`
2	the PC at time 24 = 6
3	value of cell 4 at time 24 = 3

Proof Table

#	Claim	Reason
1	not (4 = 2)	not (4 = 2) (Fixed Value Statement)
2	value of cell 4 at time (24 + 1) = value of cell 4 at time 24	if instruction #6 is `addi dst=2 src=3 imm=0` and the PC at time 24 = 6 and not (4 = 2), then value of cell 4 at time (24 + 1) = value of cell 4 at time 24 (ADDI Instruction Property 2)
3	24 + 1 = 25	24 + 1 = 25 (Fixed Value Statement)
4	value of cell 4 at time (24 + 1) = value of cell 4 at time 25	if 24 + 1 = 25, then value of cell 4 at time (24 + 1) = value of cell 4 at time 25 (Substitution)
5	value of cell 4 at time 25 = value of cell 4 at time 24	if value of cell 4 at time (24 + 1) = value of cell 4 at time 25 and value of cell 4 at time (24 + 1) = value of cell 4 at time 24, then value of cell 4 at time 25 = value of cell 4 at time 24 (Transitive Property of Equality Variation 2)
6	value of cell 4 at time 25 = 3	if value of cell 4 at time 25 = value of cell 4 at time 24 and value of cell 4 at time 24 = 3, then value of cell 4 at time 25 = 3 (Transitive Property of Equality)

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