Proof: Distribute Half

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(1 / 2) + (1 / 2) = 1	(1 / 2) + (1 / 2) = 1 (Fixed Value Statement)
2	a ⋅ ((1 / 2) + (1 / 2)) = a ⋅ 1	if (1 / 2) + (1 / 2) = 1, then a ⋅ ((1 / 2) + (1 / 2)) = a ⋅ 1 (Multiplicative Property of Equality Variation 1)
3	a ⋅ 1 = a	a ⋅ 1 = a (Multiplicative Identity)
4	a ⋅ ((1 / 2) + (1 / 2)) = a	if a ⋅ ((1 / 2) + (1 / 2)) = a ⋅ 1 and a ⋅ 1 = a, then a ⋅ ((1 / 2) + (1 / 2)) = a (Transitive Property of Equality)
5	(a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a ⋅ ((1 / 2) + (1 / 2))	(a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a ⋅ ((1 / 2) + (1 / 2)) (Distributive Property Variation 4)
6	(a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a	if (a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a ⋅ ((1 / 2) + (1 / 2)) and a ⋅ ((1 / 2) + (1 / 2)) = a, then (a ⋅ (1 / 2)) + (a ⋅ (1 / 2)) = a (Transitive Property of Equality)

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