commute

Examples of commutation

commutation
As we know, cut-elimination involves many commutations of rules.
Here the commutation relations (1.1) translate into the compatibility condition that is satisfied by with respect to the labeling.
In this appendix, we prove two commutation results on abstract relations, which are folklore.
The main mechanism that increases order is commutation.
We have used a commutation rule in the first step of transformation, and a composition rule in the second.
We could apply it only if we were seeking to determine the moment in time when the commutation happens.
Indeed, minimal pair and commutation tests, techniques commonly used in contemporary sociolinguistic studies, generally confirm the truth of this conclusion.
Thus, the commutation arcing interference can be eliminated by using suitable bypass capacitors and properly isolating the electronic circuits dealing with sensitive feedback signals.
A crucial property of the translation presented here is that it enjoys a commutation property with respect to -reduction.
The commutation theorem is usually presented in the weaker following form, where => stands for one step of parallel reduction.
In a logical circuit, for instance, every commutation supposes a loss of charge and the dissipated power appears as an escape of heat.
Of course this supposes some commutation of the other logical connectives with provability; conjunction commutes with provability already in the classical case.
Then the following diagram commutes; this is a consequence of the commutation of diagram 17.
They include composition rules, commutation rules, and the rule of clashing.
The next step is to show that the flows ft and s satisfy the following commutation relation.
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