Proof: Byte 3 Stays the Same 13

Let's prove the following theorem:

if the following are true:

instruction #7 is addi dst=4 src=4 imm=1
the PC at time 13 = 7
value of cell 3 at time 13 = 2

then value of cell 3 at time 14 = 2

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #7 is `addi dst=4 src=4 imm=1`
2	the PC at time 13 = 7
3	value of cell 3 at time 13 = 2

Proof Table

#	Claim	Reason
1	not (3 = 4)	not (3 = 4) (Fixed Value Statement)
2	value of cell 3 at time (13 + 1) = value of cell 3 at time 13	if instruction #7 is `addi dst=4 src=4 imm=1` and the PC at time 13 = 7 and not (3 = 4), then value of cell 3 at time (13 + 1) = value of cell 3 at time 13 (ADDI Instruction Property 2)
3	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
4	value of cell 3 at time (13 + 1) = value of cell 3 at time 14	if 13 + 1 = 14, then value of cell 3 at time (13 + 1) = value of cell 3 at time 14 (Substitution)
5	value of cell 3 at time 14 = value of cell 3 at time 13	if value of cell 3 at time (13 + 1) = value of cell 3 at time 14 and value of cell 3 at time (13 + 1) = value of cell 3 at time 13, then value of cell 3 at time 14 = value of cell 3 at time 13 (Transitive Property of Equality Variation 2)
6	value of cell 3 at time 14 = 2	if value of cell 3 at time 14 = value of cell 3 at time 13 and value of cell 3 at time 13 = 2, then value of cell 3 at time 14 = 2 (Transitive Property of Equality)

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