Proof: Addition Substitution
Let's prove the following theorem:
if the following are true:
- a = x
- b = y
- c = z
- z = x + y
then c = a + b
Proof:
Given
| 1 | a = x |
|---|---|
| 2 | b = y |
| 3 | c = z |
| 4 | z = x + y |
| # | Claim | Reason |
|---|---|---|
| 1 | a + b = x + y | if a = x and b = y, then a + b = x + y |
| 2 | c = x + y | if c = z and z = x + y, then c = x + y |
| 3 | c = a + b | if c = x + y and a + b = x + y, then c = a + b |
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