Proof: Reorder Terms 6

Let's prove the following theorem:

if the following are true:
  • ((a + b) + a) + b = 360
  • not (2 = 0)

then a + b = 180

Proof:

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Given
1 ((a + b) + a) + b = 360
2 not (2 = 0)
Proof Table
# Claim Reason
1 ((a + b) + a) + b = (a + b) ⋅ 2 ((a + b) + a) + b = (a + b) ⋅ 2
2 (a + b) ⋅ 2 = 360 if ((a + b) + a) + b = (a + b) ⋅ 2 and ((a + b) + a) + b = 360, then (a + b) ⋅ 2 = 360
3 a + b = 360 / 2 if (a + b) ⋅ 2 = 360 and not (2 = 0), then a + b = 360 / 2
4 360 / 2 = 180 360 / 2 = 180
5 a + b = 180 if a + b = 360 / 2 and 360 / 2 = 180, then a + b = 180

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