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