Proof: Byte 1 Stays the Same 1

Let's prove the following theorem:

if the following are true:

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

then value of cell 1 at time 2 = 0

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

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

Proof Table

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

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