Proof: Simplify Rearrange Sum 6
Let's prove the following theorem:
if the following are true:
- x = c + d
- y = e + f
then ((a + b) + (c + d)) + (e + f) = ((a + b) + x) + y
Proof:
Given
| 1 | x = c + d |
|---|---|
| 2 | y = e + f |
| # | Claim | Reason |
|---|---|---|
| 1 | ((a + b) + (c + d)) + (e + f) = ((a + b) + (c + d)) + y | if y = e + f, then ((a + b) + (c + d)) + (e + f) = ((a + b) + (c + d)) + y |
| 2 | (a + b) + (c + d) = (a + b) + x | if x = c + d, then (a + b) + (c + d) = (a + b) + x |
| 3 | ((a + b) + (c + d)) + (e + f) = ((a + b) + x) + y | if ((a + b) + (c + d)) + (e + f) = ((a + b) + (c + d)) + y and (a + b) + (c + d) = (a + b) + x, then ((a + b) + (c + d)) + (e + f) = ((a + b) + x) + y |
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