Proof: Algebra

Let's prove the following theorem:

if the following are true:
  • a = (b + c) + d
  • b = x + y

then a = ((x + y) + c) + d

Proof:

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Given
1 a = (b + c) + d
2 b = x + y
Proof Table
# Claim Reason
1 b + c = (x + y) + c if b = x + y, then b + c = (x + y) + c
2 a = ((x + y) + c) + d if a = (b + c) + d and b + c = (x + y) + c, then a = ((x + y) + c) + d

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