Proof: Term 1 Substitution
Let's prove the following theorem:
if the following are true:
- a = b + c
- b = d
then a = d + c
Proof:
Given
| 1 | a = b + c |
|---|---|
| 2 | b = d |
| # | Claim | Reason |
|---|---|---|
| 1 | b + c = c + b | b + c = c + b |
| 2 | a = c + b | if a = b + c and b + c = c + b, then a = c + b |
| 3 | a = c + d | if a = c + b and b = d, then a = c + d |
| 4 | c + d = d + c | c + d = d + c |
| 5 | a = d + c | if a = c + d and c + d = d + c, then a = d + c |
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