Proof: Multiplication Property 3
Let's prove the following theorem:
(b / c) ⋅ c = b
Proof:
| # | Claim | Reason |
|---|---|---|
| 1 | (1 / c) ⋅ c = 1 | (1 / c) ⋅ c = 1 |
| 2 | ((1 / c) ⋅ c) ⋅ b = 1 ⋅ b | if (1 / c) ⋅ c = 1, then ((1 / c) ⋅ c) ⋅ b = 1 ⋅ b |
| 3 | ((1 / c) ⋅ c) ⋅ b = (b ⋅ (1 / c)) ⋅ c | ((1 / c) ⋅ c) ⋅ b = (b ⋅ (1 / c)) ⋅ c |
| 4 | (b ⋅ (1 / c)) ⋅ c = 1 ⋅ b | if ((1 / c) ⋅ c) ⋅ b = (b ⋅ (1 / c)) ⋅ c and ((1 / c) ⋅ c) ⋅ b = 1 ⋅ b, then (b ⋅ (1 / c)) ⋅ c = 1 ⋅ b |
| 5 | 1 ⋅ b = b | 1 ⋅ b = b |
| 6 | (b ⋅ (1 / c)) ⋅ c = b | if (b ⋅ (1 / c)) ⋅ c = 1 ⋅ b and 1 ⋅ b = b, then (b ⋅ (1 / c)) ⋅ c = b |
| 7 | b ⋅ (1 / c) = b / c | b ⋅ (1 / c) = b / c |
| 8 | (b / c) ⋅ c = b | if b ⋅ (1 / c) = b / c and (b ⋅ (1 / c)) ⋅ c = b, then (b / c) ⋅ c = b |
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