Proof: Add Associative

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	((a + b) + c) + d = (a + b) + (c + d)	((a + b) + c) + d = (a + b) + (c + d) (Associative Property of Addition)
2	(a + b) + (c + d) = a + (b + (c + d))	(a + b) + (c + d) = a + (b + (c + d)) (Associative Property of Addition)
3	b + (c + d) = (b + c) + d	b + (c + d) = (b + c) + d (associative)
4	(a + b) + (c + d) = a + ((b + c) + d)	if (a + b) + (c + d) = a + (b + (c + d)) and b + (c + d) = (b + c) + d, then (a + b) + (c + d) = a + ((b + c) + d) (Term 2 Substitution)
5	((a + b) + c) + d = a + ((b + c) + d)	if ((a + b) + c) + d = (a + b) + (c + d) and (a + b) + (c + d) = a + ((b + c) + d), then ((a + b) + c) + d = a + ((b + c) + d) (Transitive Property of Equality)

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