Proof: Division Substitution2
Let's prove the following theorem:
if the following are true:
- x = i
- y = j
- z = k
- k = i / j
then z = x / y
Proof:
Given
| 1 | x = i |
|---|---|
| 2 | y = j |
| 3 | z = k |
| 4 | k = i / j |
| # | Claim | Reason |
|---|---|---|
| 1 | z = i / j | if k = i / j and z = k, then z = i / j |
| 2 | i / j = x / y | if y = j and x = i, then i / j = x / y |
| 3 | z = x / y | if i / j = x / y and z = i / j, then z = x / y |
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