Proof: Substitution 14
Let's prove the following theorem:
if the following are true:
- x = a
- x ⋅ y = b
then a ⋅ y = b
Proof:
Given
| 1 | x = a |
|---|---|
| 2 | x ⋅ y = b |
| # | Claim | Reason |
|---|---|---|
| 1 | b = x ⋅ y | if x ⋅ y = b, then b = x ⋅ y |
| 2 | b = a ⋅ y | if b = x ⋅ y and x = a, then b = a ⋅ y |
| 3 | a ⋅ y = b | if b = a ⋅ y, then a ⋅ y = b |
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