Proof: Subtract 1

Let's prove the following theorem:

Proof:

Proof Table

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

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