MATH.4:8 - Common Anti-Patterns and How to Avoid Them

Prove existence while omitting the requested witness. Recover the producing operation in each case. If the argument supplies no such operation, keep its existence conclusion and return the remaining construction question.

Fill an uncovered case with an arbitrary value. A total expression can still violate the specification. Check the value under the case’s premises or expose the failed condition, as with division by zero.

Use an induction hypothesis too weak for the step. The tree’s fixed-root-color attempt fails at the new edges. Quantify the needed color parameter and establish the stronger base and step.

Recurse on an unchanged input. The finite-constituent argument no longer establishes termination. Change the recursive calls or obtain a different well-founded argument.

Transfer the proof after changing the input’s formation. The extra edge in the triangle is absent from the tree constructors. Reopen that new case before claiming the property for the larger family.