Proof: Inequality Change
Let's prove the following theorem:
if the following are true:
- a > b
- c < 0
then a ⋅ c < b ⋅ c
Proof:
Given
| 1 | a > b |
|---|---|
| 2 | c < 0 |
| # | Claim | Reason |
|---|---|---|
| 1 | b ⋅ c > a ⋅ c | if c < 0 and a > b, then b ⋅ c > a ⋅ c |
| 2 | a ⋅ c < b ⋅ c | if b ⋅ c > a ⋅ c, then a ⋅ c < b ⋅ c |
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