Proof: Reduce Addition

Let's prove the following theorem:

if the following are true:
  • ((a + a) + a) + a = 360
  • not (4 = 0)

then a = 90

Proof:

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Given
1 ((a + a) + a) + a = 360
2 not (4 = 0)
Proof Table
# Claim Reason
1 ((a + a) + a) + a = a ⋅ 4 ((a + a) + a) + a = a ⋅ 4
2 a ⋅ 4 = 360 if ((a + a) + a) + a = 360 and ((a + a) + a) + a = a ⋅ 4, then a ⋅ 4 = 360
3 a = 360 / 4 if not (4 = 0) and a ⋅ 4 = 360, then a = 360 / 4
4 360 / 4 = 90 360 / 4 = 90
5 a = 90 if 360 / 4 = 90 and a = 360 / 4, then a = 90

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