Proof: Multiply 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	((a + b) + a) + b = (a + b) + (a + b)	((a + b) + a) + b = (a + b) + (a + b) (Associative Property of Addition)
2	(a + b) + (a + b) = (a + b) ⋅ 2	(a + b) + (a + b) = (a + b) ⋅ 2 (addition_theorem)
3	((a + b) + a) + b = (a + b) ⋅ 2	if ((a + b) + a) + b = (a + b) + (a + b) and (a + b) + (a + b) = (a + b) ⋅ 2, then ((a + b) + a) + b = (a + b) ⋅ 2 (Transitive Property of Equality)

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