C.29.1:4.1 - Recover the result and the direction in which it will be used
Start with the receiving question. Say what is to be determined and what difference the answer makes: whether another reservation is allowed, the cost of a chosen route, the least possible route cost, or a temperature bound at a specified time. These questions can concern the same objects and require different retained information.
Recover the source result together with the ingredients that produced it:
- the allowed inputs and the meaning of their quantities;
- the operations or relations used in the inference;
- the premises and operation conditions on which the conclusion depends.
Use an existing derivation when these ingredients are available. If an explanation gives only a final formula, recover the missing construction or argument through B.5:4.2 and B.5:4.3. The transfer comparison begins once the required source step is clear enough to reproduce.
Then name the direction of use. There are several common possibilities.
| Intended use | Correspondence to establish |
|---|---|
| Represent a source result in another account | Source inputs and steps have receiving counterparts, with the needed conclusion preserved. |
| Calculate in another account and answer about a source input | The receiving calculation, applied to that input’s representation, returns the sought source quantity or a justified bound on it. |
| Choose a receiving solution and carry it back as an action | The selected receiving solution has an allowed source counterpart, and the returned counterpart has the claimed properties. |
| Transfer a theorem to an entire receiving domain | The theorem’s premises and inference steps survive, and the domain claimed in the conclusion is covered. |
The last two uses are stronger than merely mapping source cases forward. Keeping the direction explicit prevents an answer about a relaxed problem from becoming an unsupported action recommendation.