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