Given that:

not (b = 0)

not (2 = 0)

not (b ⋅ 2 = 0)

Prove that:

(a ⋅ 2) / (b ⋅ 2) = a / b

The following properties may be helpful:

a ⋅ 1 = a
2 / 2 = 1
if the following are true:
- a ⋅ b = c
- d = b
then a ⋅ d = c
if the following are true:
- not (b = 0)
- not (d = 0)
- not (b ⋅ d = 0)
then (a / b) ⋅ (c / d) = (a ⋅ c) / (b ⋅ d)
if the following are true:
- a = b
- a = c
then b = c

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.

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