Let's prove the following theorem:

if the following are true:

then a = b ⋅ (1 / 2)

Given

1	a ⋅ 2 = b
2	not (2 = 0)

Proof Table

#	Claim	Reason
1	(a ⋅ 2) ⋅ (1 / 2) = b ⋅ (1 / 2)	if a ⋅ 2 = b, then (a ⋅ 2) ⋅ (1 / 2) = b ⋅ (1 / 2) (Multiplicative Property of Equality)
2	(a ⋅ 2) ⋅ (1 / 2) = a	if not (2 = 0), then (a ⋅ 2) ⋅ (1 / 2) = a (Simplify 2)
3	a = b ⋅ (1 / 2)	if (a ⋅ 2) ⋅ (1 / 2) = b ⋅ (1 / 2) and (a ⋅ 2) ⋅ (1 / 2) = a, then a = b ⋅ (1 / 2) (Transitive Property of Equality Variation 2)

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