*3.15. Theorem C I I* |→ *K*

**Proof.** Based on (25) and (19), (21) we can see that {*CII*}⊂{*K*}. There is even equality with the particular model of the result principle {*CII*} = {*K*}<sup>↓</sup> <sup>0</sup><*ηm*<<sup>1</sup> for *η<sup>m</sup>* = *ηC*.

The analyzed implication is a weaker version of the implication (34):

$$
\eta \le \eta\_{\mathbb{C}} = 1 - \frac{T\_1}{T\_2} < 1. \tag{35}
$$

Thus, the *K* principle is weaker than the *CII* principle. Since the *K* principle applies essentially to engine processes (or the absence of *perpetuum mobile* type II), the proof can be limited to processes of this type. On the other hand, the generality of the proof is secured by the fact that one model is included in the other model.
