Proof: Divide Substitute 4
Let's prove the following theorem:
if the following are true:
- a = w
- b = x
- c = y
- d = z
then (a - b) / (c - d) = (w - x) / (y - z)
Proof:
Given
| 1 | a = w |
|---|---|
| 2 | b = x |
| 3 | c = y |
| 4 | d = z |
| # | Claim | Reason |
|---|---|---|
| 1 | a - b = w - x | if b = x and a = w, then a - b = w - x |
| 2 | c - d = y - z | if d = z and c = y, then c - d = y - z |
| 3 | (a - b) / (c - d) = (w - x) / (y - z) | if c - d = y - z and a - b = w - x, then (a - b) / (c - d) = (w - x) / (y - z) |
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