Idempotency of entailment
Idempotency of entailment is a property of logical systems that states that one may derive the same consequences from many instances of a hypothesis as from just one. This property can be captured by a structural rule called contraction, and in such systems one may say that entailment is idempotent if and only if contraction is an admissible rule.
Rule of contraction: from
is derived
Or in sequent calculus notation,
In linear and affine logic, entailment is not idempotent.
