8.4. Theorem

Let states s1⚪ .. sN⚪, their multiple s0⚪ = s1⚪ × … × sN⚪ and prototypes s1◎ .. sN◎.

If there is a states s0◎ = s1◎ ´ .. ´ sN◎, then it is a prototype for s0⚪

s0⚪ ⊴ s0◎

Evidence

Suppose the opposite - in the composition of s0⚪ and s0◎ there is a certain variable, which has different values. Such a variable must belong to some si⚪ from s1⚪ .. sN⚪.

The same value must be s0⚪ and its prototyp si◎ from s1◎ .. sN◎.

Hence, s0◎ must contain it, which is in contradiction with the original assumption about the difference in the values of common variables. █

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