Proof: Move Terms Around
Let's prove the following theorem:
if n ⋅ p = m, then m = p ⋅ n
Proof:
Given
| 1 | n ⋅ p = m |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | m = n ⋅ p | if n ⋅ p = m, then m = n ⋅ p |
| 2 | n ⋅ p = p ⋅ n | n ⋅ p = p ⋅ n |
| 3 | m = p ⋅ n | if n ⋅ p = p ⋅ n and m = n ⋅ p, then m = p ⋅ n |
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