Invalid syntactic shortcut
Definition
An invalid syntactic shortcut is a proof step that looks like a familiar manipulation but is not licensed by the relevant rule or assumptions.
Explanation
Ask what rule the step uses and whether its conditions hold. A line can look ordinary while changing a quantifier’s scope, substituting a value without justification, or applying an inference to the wrong premises.
To check it, write the claimed rule separately and match each of its inputs with the proof. If the match fails, the derivation needs repair.
An invalid derivation can end at a true conclusion. The problem is that the steps do not establish it. That distinction matters when grading proofs and when evaluating chatbot feedback.
Scope and evidence
This is a teaching label in the discrete mathematics materials. It describes the validity of a step, rather than proving that the final claim is false.
Sources
Related concepts
Contextual embedding · Hallucination autopsy procedure · Axiom reversion