Proof: Apply Associative Multiply
Let's prove the following theorem:
if b ⋅ c = d, then (a ⋅ b) ⋅ c = a ⋅ d
Proof:
Given
| 1 | b ⋅ c = d |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c) | (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c) |
| 2 | a ⋅ (b ⋅ c) = a ⋅ d | if b ⋅ c = d, then a ⋅ (b ⋅ c) = a ⋅ d |
| 3 | (a ⋅ b) ⋅ c = a ⋅ d | if a ⋅ (b ⋅ c) = a ⋅ d and (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c), then (a ⋅ b) ⋅ c = a ⋅ d |
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