Proof: Byte 3 Stays the Same 9

Let's prove the following theorem:

if the following are true:

instruction #5 is beq left=3 right=4 imm=1
the PC at time 9 = 5
value of cell 3 at time 9 = 3

then value of cell 3 at time 10 = 3

Proof:

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Given

1	instruction #5 is `beq left=3 right=4 imm=1`
2	the PC at time 9 = 5
3	value of cell 3 at time 9 = 3

Proof Table

#	Claim	Reason
1	value of cell 3 at time (9 + 1) = value of cell 3 at time 9	if instruction #5 is `beq left=3 right=4 imm=1` and the PC at time 9 = 5, then value of cell 3 at time (9 + 1) = value of cell 3 at time 9 (BEQ Instruction Property 3)
2	9 + 1 = 10	9 + 1 = 10 (Fixed Value Statement)
3	value of cell 3 at time (9 + 1) = value of cell 3 at time 10	if 9 + 1 = 10, then value of cell 3 at time (9 + 1) = value of cell 3 at time 10 (Substitution)
4	value of cell 3 at time 10 = value of cell 3 at time 9	if value of cell 3 at time (9 + 1) = value of cell 3 at time 10 and value of cell 3 at time (9 + 1) = value of cell 3 at time 9, then value of cell 3 at time 10 = value of cell 3 at time 9 (Transitive Property of Equality Variation 2)
5	value of cell 3 at time 10 = 3	if value of cell 3 at time 10 = value of cell 3 at time 9 and value of cell 3 at time 9 = 3, then value of cell 3 at time 10 = 3 (Transitive Property of Equality)

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