Proof: Multiplication Theorem
Let's prove the following theorem:
if not (c = 0), then (b ⋅ c) / c = b
Proof:
Given
| 1 | not (c = 0) |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | (b / c) ⋅ c = b | if not (c = 0), then (b / c) ⋅ c = b |
| 2 | (b / c) ⋅ c = (b ⋅ c) / c | (b / c) ⋅ c = (b ⋅ c) / c |
| 3 | (b ⋅ c) / c = b | if (b / c) ⋅ c = (b ⋅ c) / c and (b / c) ⋅ c = b, then (b ⋅ c) / c = b |
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