Proof: Double to Half
Let's prove the following theorem:
if the following are true:
- a + a = b
- not (2 = 0)
then a = b ⋅ (1 / 2)
Proof:
Given
| 1 | a + a = b |
|---|---|
| 2 | not (2 = 0) |
| # | Claim | Reason |
|---|---|---|
| 1 | a ⋅ 2 = b | if a + a = b, then a ⋅ 2 = b |
| 2 | a = b ⋅ (1 / 2) | if not (2 = 0) and a ⋅ 2 = b, then a = b ⋅ (1 / 2) |
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