Proof: Whole is Greater Than Parts

Let's prove the following theorem:

if the following are true:
  • a = b + c
  • b > 0

then a > c

Proof:

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Given
1 a = b + c
2 b > 0
Proof Table
# Claim Reason
1 b + c = c + b b + c = c + b
2 a = c + b if a = b + c and b + c = c + b, then a = c + b
3 a > c if a = c + b and b > 0, then a > c

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