MATH.12:4.5 - Obtain the result and use its justification

Apply the extracted operation to the input of interest. Follow its reductions far enough to obtain the requested value, and use the proof’s retained relation to justify that value.

A worked input checks that the expression can be followed. The general output claim comes from the construction and its proof under the stated assumptions. Where the representation can overflow, round or reorder dependent updates, establish that its operations preserve the mathematical result needed here.

Retain intermediate results when recomputation would matter. A proof transformation that preserves a function’s output can still duplicate an expensive calculation. Compare implementation choices under the same output requirement.

For work on another subject, use C.29 to establish the correspondence between the mathematical construction and that subject. C.29.3 connects a computation with its input preparation, execution and result interpretation. A mathematical function transformation can inform a change of method while the changed method still needs its physical, resource and interaction conditions.

Stop with the required object, a reusable obtaining operation with its property, or the particular premise that still lacks a construction.