Proof: Simplify 4

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	a + (b + (b ⋅ (-1))) = a	a + (b + (b ⋅ (-1))) = a (subtract_both_sides_pre_2)
2	a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1))	a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1)) (associative)
3	(a + b) + (b ⋅ (-1)) = a	if a + (b + (b ⋅ (-1))) = a and a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1)), then (a + b) + (b ⋅ (-1)) = a (Transitive Property of Equality Variation 2)

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