Proof: Inverse Product Theorem

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	a / a = 1	if not (a = 0), then a / a = 1 (Multiplicative Inverse Property)
2	a / a = a ⋅ (1 / a)	a / a = a ⋅ (1 / a) (Division is Multiplication by Inverse)
3	a ⋅ (1 / a) = (1 / a) ⋅ a	a ⋅ (1 / a) = (1 / a) ⋅ a (Commutative Property of Multiplication)
4	a / a = (1 / a) ⋅ a	if a / a = a ⋅ (1 / a) and a ⋅ (1 / a) = (1 / a) ⋅ a, then a / a = (1 / a) ⋅ a (Transitive Property of Equality)
5	(1 / a) ⋅ a = 1	if a / a = (1 / a) ⋅ a and a / a = 1, then (1 / a) ⋅ a = 1 (Transitive Property of Equality Variation 2)

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