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


 * A,C,C → B

is derived
 * A,C → B.

Or in sequent calculus notation,
 * $$\frac{\Gamma,C,C\vdash B}{\Gamma,C\vdash B}$$

In linear and affine logic, entailment is not idempotent.