Proof: Inverse Product Theorem
Let's prove the following theorem:
(1 / a) ⋅ a = 1
Proof:
| # | Claim | Reason |
|---|---|---|
| 1 | a / a = 1 | a / a = 1 |
| 2 | a / a = a ⋅ (1 / a) | a / a = a ⋅ (1 / a) |
| 3 | a ⋅ (1 / a) = (1 / a) ⋅ a | a ⋅ (1 / a) = (1 / a) ⋅ a |
| 4 | a / a = (1 / a) ⋅ a | if a / a = a ⋅ (1 / a) and a ⋅ (1 / a) = (1 / a) ⋅ a, then a / a = (1 / a) ⋅ a |
| 5 | (1 / a) ⋅ a = 1 | if a / a = (1 / a) ⋅ a and a / a = 1, then (1 / a) ⋅ a = 1 |
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