Proof: Simplify 4

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	b + (b ⋅ (-1)) = 0	b + (b ⋅ (-1)) = 0 (Additive Inverse Property)
2	a + (b + (b ⋅ (-1))) = a + 0	if b + (b ⋅ (-1)) = 0, then a + (b + (b ⋅ (-1))) = a + 0 (Substitution)
3	a + 0 = a	a + 0 = a (Additive Identity)
4	a + (b + (b ⋅ (-1))) = a	if a + (b + (b ⋅ (-1))) = a + 0 and a + 0 = a, then a + (b + (b ⋅ (-1))) = a (Transitive Property of Equality)
5	a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1))	a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1)) (associative)
6	(a + b) + (b ⋅ (-1)) = a	if a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1)) and a + (b + (b ⋅ (-1))) = a, then (a + b) + (b ⋅ (-1)) = a (Transitive Property of Equality Variation 2)

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