 While provers (sādhana), i.e., logical reasons and examples, can of course be expressed in words, as in a “public” inference-for-others, they are not themselves words. Although Dharmakīrti et al. speak in terms of one state of affairs, or one entity (artha), proving another, in fact the picture has all the complex features of the scheme-content gap and its bridges: logical reasoning is a mental process that directly treats of fictional proxies, i.e., concepts, which are in turn connected in apoha-fashion to real particular entities. Not surprisingly, the idea that provers are apoha-properties rather than words has its philosophical complexities. When do we have the same property and when do they differ? When a pervasion is bidirectional, or "equal" (samavyāpti), as in the case of being impermanent (anityatva) and being produced (kṛtakatva), it’s quite easy to see that the impermanent particulars will be identical with the produced particulars. Given that the bidirectional pervasion analyzes as “for all x, x is produced if and only if x is impermanent”, the extension of the two concepts (i.e., the set of impermanent particulars and the set of produced particulars) is the same for Buddhists. Nonetheless, substitutivity of one term for the other would seem to lead to an invalid inference where the premises are true but the conclusion is not. To bring out the problem, take the following tempting, but invalid, inference: