Proof: Multiply Both Sides 2
Let's prove the following theorem:
if the following are true:
- a = b / c
- not (c = 0)
then c ⋅ a = b
Proof:
Given
| 1 | a = b / c |
|---|---|
| 2 | not (c = 0) |
| # | Claim | Reason |
|---|---|---|
| 1 | a ⋅ c = (b / c) ⋅ c | if a = b / c, then a ⋅ c = (b / c) ⋅ c |
| 2 | (b / c) ⋅ c = b | if not (c = 0), then (b / c) ⋅ c = b |
| 3 | a ⋅ c = b | if (b / c) ⋅ c = b and a ⋅ c = (b / c) ⋅ c, then a ⋅ c = b |
| 4 | a ⋅ c = c ⋅ a | a ⋅ c = c ⋅ a |
| 5 | c ⋅ a = b | if a ⋅ c = b and a ⋅ c = c ⋅ a, then c ⋅ a = b |
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