Proof: Byte 4 Stays the Same 3

Let's prove the following theorem:

if the following are true:

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

then value of cell 4 at time 4 = 0

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

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

Proof Table

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

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