Proof: Simplify 2

Let's prove the following theorem:

if not (2 = 0), then (a ⋅ 2) ⋅ (1 / 2) = a

Proof:

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Given
1 not (2 = 0)
Proof Table
# Claim Reason
1 (a ⋅ 2) ⋅ (1 / 2) = a ⋅ 1 if not (2 = 0), then (a ⋅ 2) ⋅ (1 / 2) = a ⋅ 1
2 a ⋅ 1 = a a ⋅ 1 = a
3 (a ⋅ 2) ⋅ (1 / 2) = a if (a ⋅ 2) ⋅ (1 / 2) = a ⋅ 1 and a ⋅ 1 = a, then (a ⋅ 2) ⋅ (1 / 2) = a

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