Proof: Computer At Offset Z

Let's prove the following theorem:

if the following are true:

there is a computer at location x: x y: y z: z and time: t
z = a + b

then there is a computer at location x: x y: y z: (a + b) and time: t

Proof:

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Given

1	there is a computer at location x: x y: y z: z and time: t
2	z = a + b

Proof Table

#	Claim	Reason
1	there is a computer at location x: x y: y z: z and time: t = there is a computer at location x: x y: y z: (a + b) and time: t	if z = a + b, then there is a computer at location x: x y: y z: z and time: t = there is a computer at location x: x y: y z: (a + b) and time: t (Substitution)
2	there is a computer at location x: x y: y z: (a + b) and time: t	if there is a computer at location x: x y: y z: z and time: t and there is a computer at location x: x y: y z: z and time: t = there is a computer at location x: x y: y z: (a + b) and time: t, then there is a computer at location x: x y: y z: (a + b) and time: t (Truth Propagation Property)

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