Proof: Simplify

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	0 + (a ⋅ 2) = a ⋅ 2	0 + (a ⋅ 2) = a ⋅ 2 (zero_plus_a)
2	(0 + (a ⋅ 2)) / 2 = (a ⋅ 2) / 2	if 0 + (a ⋅ 2) = a ⋅ 2, then (0 + (a ⋅ 2)) / 2 = (a ⋅ 2) / 2 (Division Property of Equality)
3	(a ⋅ 2) / 2 = a ⋅ (2 / 2)	(a ⋅ 2) / 2 = a ⋅ (2 / 2) (associative_property)
4	2 / 2 = 1	2 / 2 = 1 (Fixed Value Statement)
5	a ⋅ (2 / 2) = a ⋅ 1	if 2 / 2 = 1, then a ⋅ (2 / 2) = a ⋅ 1 (Multiplicative Property of Equality Variation 1)
6	a ⋅ 1 = a	a ⋅ 1 = a (Multiplicative Identity)
7	a ⋅ (2 / 2) = a	if a ⋅ (2 / 2) = a ⋅ 1 and a ⋅ 1 = a, then a ⋅ (2 / 2) = a (Transitive Property of Equality)
8	(a ⋅ 2) / 2 = a	if (a ⋅ 2) / 2 = a ⋅ (2 / 2) and a ⋅ (2 / 2) = a, then (a ⋅ 2) / 2 = a (Transitive Property of Equality)
9	(0 + (a ⋅ 2)) / 2 = a	if (0 + (a ⋅ 2)) / 2 = (a ⋅ 2) / 2 and (a ⋅ 2) / 2 = a, then (0 + (a ⋅ 2)) / 2 = a (Transitive Property of Equality)

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