Proof: Byte 5 Stays the Same 13

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 13 = 5
value of cell 5 at time 13 = 21

then value of cell 5 at time 14 = 21

Proof:

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Given

1	instruction #5 is `beq left=3 right=4 imm=1`
2	the PC at time 13 = 5
3	value of cell 5 at time 13 = 21

Proof Table

#	Claim	Reason
1	value of cell 5 at time (13 + 1) = value of cell 5 at time 13	if instruction #5 is `beq left=3 right=4 imm=1` and the PC at time 13 = 5, then value of cell 5 at time (13 + 1) = value of cell 5 at time 13 (BEQ Instruction Property 3)
2	13 + 1 = 14	13 + 1 = 14 (Fixed Value Statement)
3	value of cell 5 at time (13 + 1) = value of cell 5 at time 14	if 13 + 1 = 14, then value of cell 5 at time (13 + 1) = value of cell 5 at time 14 (Substitution)
4	value of cell 5 at time 14 = value of cell 5 at time 13	if value of cell 5 at time (13 + 1) = value of cell 5 at time 14 and value of cell 5 at time (13 + 1) = value of cell 5 at time 13, then value of cell 5 at time 14 = value of cell 5 at time 13 (Transitive Property of Equality Variation 2)
5	value of cell 5 at time 14 = 21	if value of cell 5 at time 14 = value of cell 5 at time 13 and value of cell 5 at time 13 = 21, then value of cell 5 at time 14 = 21 (Transitive Property of Equality)

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