Proof: Byte 4 Stays the Same 11

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 11 = 5
value of cell 4 at time 11 = 1

then value of cell 4 at time 12 = 1

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 11 = 5
3	value of cell 4 at time 11 = 1

Proof Table

#	Claim	Reason
1	not (4 = 1)	not (4 = 1) (Fixed Value Statement)
2	value of cell 4 at time (11 + 1) = value of cell 4 at time 11	if instruction #5 is `addi dst=1 src=2 imm=0` and the PC at time 11 = 5 and not (4 = 1), then value of cell 4 at time (11 + 1) = value of cell 4 at time 11 (ADDI Instruction Property 2)
3	11 + 1 = 12	11 + 1 = 12 (Fixed Value Statement)
4	value of cell 4 at time (11 + 1) = value of cell 4 at time 12	if 11 + 1 = 12, then value of cell 4 at time (11 + 1) = value of cell 4 at time 12 (Substitution)
5	value of cell 4 at time 12 = value of cell 4 at time 11	if value of cell 4 at time (11 + 1) = value of cell 4 at time 12 and value of cell 4 at time (11 + 1) = value of cell 4 at time 11, then value of cell 4 at time 12 = value of cell 4 at time 11 (Transitive Property of Equality Variation 2)
6	value of cell 4 at time 12 = 1	if value of cell 4 at time 12 = value of cell 4 at time 11 and value of cell 4 at time 11 = 1, then value of cell 4 at time 12 = 1 (Transitive Property of Equality)

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