Proof: Byte 1 Stays the Same 20

Let's prove the following theorem:

if the following are true:

instruction #8 is beq left=4 right=5 imm=1
the PC at time 20 = 8
value of cell 1 at time 20 = 2

then value of cell 1 at time 21 = 2

Instructions

Memory Cells

Program Counter	Time
0	0

LW Computer Simulator

Proof:

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Given

1	instruction #8 is `beq left=4 right=5 imm=1`
2	the PC at time 20 = 8
3	value of cell 1 at time 20 = 2

Proof Table

#	Claim	Reason
1	value of cell 1 at time (20 + 1) = value of cell 1 at time 20	if instruction #8 is `beq left=4 right=5 imm=1` and the PC at time 20 = 8, then value of cell 1 at time (20 + 1) = value of cell 1 at time 20 (BEQ Instruction Property 3)
2	20 + 1 = 21	20 + 1 = 21 (Fixed Value Statement)
3	value of cell 1 at time (20 + 1) = value of cell 1 at time 21	if 20 + 1 = 21, then value of cell 1 at time (20 + 1) = value of cell 1 at time 21 (Substitution)
4	value of cell 1 at time 21 = value of cell 1 at time 20	if value of cell 1 at time (20 + 1) = value of cell 1 at time 21 and value of cell 1 at time (20 + 1) = value of cell 1 at time 20, then value of cell 1 at time 21 = value of cell 1 at time 20 (Transitive Property of Equality Variation 2)
5	value of cell 1 at time 21 = 2	if value of cell 1 at time 21 = value of cell 1 at time 20 and value of cell 1 at time 20 = 2, then value of cell 1 at time 21 = 2 (Transitive Property of Equality)

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