█████ (███████████)

█████ ███████: the ████████

███ of the ████ ████████ ██████ is the ███ of ████████ $${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}=\{\dots ,-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\dots \}}$$ ████████ with ████████. For ███ ███ ████████ ${\displaystyle a}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, the ███ ${\displaystyle a+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████ an ███████; this ███████ ████████ ████ that ${\displaystyle +}$ is a ██████ █████████ on ⁠${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. The following ██████████ of ███████ ████████ █████ as a █████ for the █████ ██████ in the ██████████ below.

• For ███ ████████ ⁠${\displaystyle a}$⁠, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ███ has ⁠${\displaystyle (a+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=a+(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$⁠. █████████ in █████, ██████ ${\displaystyle a}$ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████, and ████ ██████ the ██████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ the ████ █████ ██████ as ██████ ${\displaystyle a}$ to the ███ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. This ████████ is █████ as █████████████.
• If ${\displaystyle a}$ is ███ ███████, ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+a=a}$ and ⁠${\displaystyle a+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=a}$⁠. ████ is ██████ the ████████ ███████ of ████████ because ██████ it to ███ ███████ ███████ the ████ ███████.
• For █████ ███████ ⁠${\displaystyle a}$⁠, there is an ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that ${\displaystyle a+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+a=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. The ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████ the ███████ ███████ of the ███████ ${\displaystyle a}$ and is ███████ ⁠${\displaystyle -a}$⁠.

The ████████, ████████ with the █████████ ⁠${\displaystyle +}$⁠, ████ a ████████████ ██████ █████████ to a █████ █████ ███████ ███████ ██████████ ███████. To █████████████ ██████████ █████ ██████████ as a ██████████, the following ██████████ is █████████.

██████████

A █████ is a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ with a ██████ █████████ on ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ████ ███████ "⁠${\displaystyle \cdot }$⁠", that ████████ ███ ███ ████████ ${\displaystyle a}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ████ an ███████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ███████ ⁠${\displaystyle a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ████ that the following █████ ████████████, █████ as █████ ██████, are █████████:

█████████████

For ███ ⁠${\displaystyle a}$⁠, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ███ has ⁠${\displaystyle (a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=a\cdot (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$⁠.

████████ ███████

There ██████ an ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that, for █████ ${\displaystyle a}$ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ███ has ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot a=a}$⁠ and ⁠${\displaystyle a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=a}$⁠.

████ an ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████. It is ██████ the ████████ ███████ (or █████████ ███████ ███████) of the █████.

███████ ███████

For ████ ${\displaystyle a}$ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, there ██████ an ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that ${\displaystyle a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot a=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████████ ███████.

For ████ ⁠${\displaystyle a}$⁠, the ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████; it is ██████ the ███████ of ${\displaystyle a}$ and is ████████ ███████ ⁠${\displaystyle a^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠.

████: ██████████ of the ████████ and ██████████ of ███████ ████████ are not ████ of the ██████; they are ████████████ of the █████ ██████.

████████ and ███████████

████████, a █████ is an ███████ ████ of a ███ and a ██████ █████████ on this ███ that █████████ the █████ ██████. The ███ is ██████ the ██████████ ███ of the █████, and the █████████ is ██████ the █████ █████████ or the █████ ███.

A █████ and ███ ██████████ ███ are ████ ███ █████████ ████████████ ███████. To █████ ██████████ ████████, it is ██████ to █████ ████████ by using the ████ ██████ to ██████ ████. This ████████ ████ an ████████ ███ of ████████: that the █████ is the ████ as the ███ except that it has been ████████ by ██████████ █████████ ████████ by the █████████.

For ███████, ████████ the ███ of ████ ███████ ⁠${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, which has the ██████████ of ████████ ${\displaystyle a+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ██████████████ ⁠${\displaystyle a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. ████████, ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ███, ${\displaystyle (\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>},+)}$ is a █████, and ${\displaystyle (\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>},+,\cdot )}$ is a █████. But it is ██████ to █████ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ██████ ███ of █████ █████ ███████.

The ████████ █████ of the █████ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ █████ ██████████ ███ is ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and █████ █████████ is ████████. The ██████████████ █████ of the █████ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ ${\displaystyle {\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\times }}$ █████ ██████████ ███ is the ███ of ███████ ████ ███████ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}\setminus \{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$ and █████ █████████ is ██████████████.

████ █████████, ███ ██████ of an ████████ █████ ████████ the █████ █████████ is ███████ as ████████; in this ████, the ████████ is █████████ ███████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and the ███████ of an ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ███████ ⁠${\displaystyle -\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. █████████, ███ ██████ of a ██████████████ █████ ████████ the █████ █████████ is ███████ as ██████████████; in this ████, the ████████ is █████████ ███████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and the ███████ of an ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ███████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠. In a ██████████████ █████, the █████████ ██████ is ███████ ███████ ████████, ██ that the █████████ is ███████ by █████████████, ${\displaystyle a\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ of ⁠${\displaystyle a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠.

The ██████████ of a █████ ████ not ███████ that ${\displaystyle a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot a}$ for ███ ████████ ${\displaystyle a}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. If this ██████████ █████████ █████, ████ the █████████ is ████ to be ███████████, and the █████ is ██████ an ███████ █████. It is a ██████ ██████████ that for an ███████ █████ ██████ ████████ or ██████████████ ████████ ███ be used, but for a ██████████ █████ ████ ██████████████ ████████ is used.

███████ █████ █████████ are ████████ used for ██████ █████ ████████ are not ███████. For a █████ █████ ████████ are █████████, the █████████ is █████ ████████ ███████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠; ████ the ████████ ███ be ███████ ██. In the ████ ████████ █████ of █████████ ██████████████ ██████, ████████ ██████, ███████████ ██████, and ████████████ ██████, the ██████ ${\displaystyle \circ }$ is █████ ███████, as for ██████████████ ██████. ████ █████ ████████ of ████████ ███ be ███████████.

██████ ███████: a ████████ █████

███ ███████ in the █████ are █████████ if ███ can be ███████ into the █████ using a ███████████ of █████████, ███████████, and ████████████. ███ ██████ is █████████ to ██████. ███████, some ███████ are █████████ to ██████████ in ████ than ███ ███, and █████ █████ ███████████ are ██████ ██████████. A ██████ has █████ ██████████. █████ are:

• the ████████ █████████ ███████ ██████████ █████████, ███████ ${\displaystyle \mathrm{<span\; word-length="2"\; class="word\; redacted">██</span>}}$;
• █████████ of the ██████ around ███ ██████ by ██°, ███°, and ███° █████████, ███████ by ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, ████████████;
• ███████████ about the ██████████ and ████████ ██████ ████ (⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠ and ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠), or through the ███ █████████ (⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠ and ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠).

█████ ██████████ are █████████. ████ █████ a █████ in the ██████ to the █████████████ █████ under the ████████. For ███████, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ a █████ to ███ ████████ ██° █████████ around the ██████'s ██████, and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ a █████ to ███ ██████████ across the ██████'s ████████ ██████ ████. █████████ ███ of █████ ██████████ █████ ███████ ████████. █████ ██████████ █████████ a █████ ██████ the ████████ █████ of ██████ ████, ███████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠. The ██████████ ███ of the █████ is the above ███ of ██████████, and the █████ █████████ is ████████ ███████████. ███ ██████████ are ████████ by █████████ ████ as █████████, that is, ████████ the █████ ███ to the ██████, and the ██████ ███ to the ██████ of the █████ ███████████. The ██████ of ██████████ █████ ${\displaystyle a}$ and ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ███████ ████████████ from █████ to ████ as ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ a}$ ("█████ the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ after ██████████ the ████████ ⁠${\displaystyle a}$⁠"). This is the █████ ████████ for the ███████████ of █████████.

A ██████ █████ █████ the ███████ of ███ ████ ████████████ ████████. For ███████, ████████ by ███° █████████ (⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠) and ████ ██████████ ████████████ (⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠) is the ████ as ██████████ a ██████████ along the ████████ (⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠). Using the above ███████, ███████████ in ████ in the ██████ █████: $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$

█████ this ███ of ██████████ and the █████████ █████████, the █████ ██████ can be ██████████ as ███████:

• ██████ █████████: ███████████ is a ██████ █████████. That is, ${\displaystyle a\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ████████ for ███ ███ ██████████ ${\displaystyle a}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. For ███████, $${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$$ That is, ████████ ███° █████████ after ██████████ ████████████ ██████ ██████████ along the ███████-████████ (⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠). ██████, █████ █████ ███████████ of ███ ██████████ █████ █████ a ████████, as can be ███████ using the ██████ █████.
• █████████████: The █████████████ █████ █████ with █████████ ████ than ███ ██████████: ████████ with █████ ████████ ⁠${\displaystyle a}$⁠, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ of ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, there are ███ ████████ ████ of using █████ █████ ██████████ in this █████ to █████████ a ████████ of the ██████. ███ of █████ ████ is to █████ ███████ ${\displaystyle a}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ into a ██████ ████████, ████ to ███████ that ████████ with ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. The █████ ███ is to █████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ████ to ███████ the █████████ ████████ with ⁠${\displaystyle a}$⁠. █████ ███ ████ ████ ██████ ████ the ████ ██████, that is, $${\displaystyle (a\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=a\circ (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}).}$$ For ███████, ${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$ can be ███████ using the ██████ █████:
• ████████ ███████: The ████████ ███████ is ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, as it ████ not ██████ ███ ████████ ${\displaystyle a}$ ████ ████████ with it ██████ on the ████ or on the █████.
• ███████ ███████: ████ ████████ has an ███████: ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, the ███████████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠ and the ███° ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ are █████ ███ ███████, because ██████████ ████ █████ ██████ the ██████ ████ to ███ ████████ ███████████. The █████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ are ████ █████'s ████████, because ████████ ██° and ████ ████████ ███° (or ████ █████) ██████ a ████████ over ███° which ██████ the ██████ █████████. This is ██████ ████████ in the █████.

In ████████ to the █████ of ████████ above, █████ the █████ of the █████████ is ██████████, it ████ ██████ in ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, as, for ███████, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ but ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠. In █████ █████, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is not ███████.

██████████ of ████████ ███████

The █████ ██████ █████ that the ████████ ███████ is ██████; that is, there ██████ ████ ███ ████████ ███████: ███ ███ ████████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of a █████ are █████, because the █████ ██████ █████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. It is ████ █████████ to █████ of the ████████ ███████ of the █████.

██████████ of ████████

The █████ ██████ ████ █████ that the ███████ of ████ ███████ is ██████. ███ a █████ ███████ ${\displaystyle a}$ have ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ as ████████. ████

█████████, it is █████████ to █████ of the ███████ of an ███████.

████████

█████ ████████ ${\displaystyle a}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of a █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, there is a ██████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to the ████████ ${\displaystyle a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██████ ${\displaystyle a^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. It ███████ that for ████ ${\displaystyle a}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ that ████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ${\displaystyle a\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████████; it is ██████ ████ ██████████████ by ${\displaystyle a}$ or ████ ███████████ by ${\displaystyle a}$.

█████████, █████ ${\displaystyle a}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, the ██████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot a=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot a^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. For ████ ${\displaystyle a}$, the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ that ████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot a}$ is a █████████ ██████ █████ ██████████████ by ${\displaystyle a}$ or █████ ███████████ by ${\displaystyle a}$.

██████████ ██████████ with ███████ ██████

The █████ ██████ for ████████ and ████████ ███ be "████████" to ██████ ████ the █████████ of a ████ ████████ and ████ ████████. From █████ ███-█████ ██████, ███ can █████ that the ████ ████████ is ████ a █████ ████████ and a ████ ███████ is ████ a █████ ███████ for the ████ ███████. Since they ██████ ███████ the ████ ██████████ as ██████, ████████████ the ██████ are not ██████.

In ██████████, ████████ █████████████ and the █████████ of a ████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (that is, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠) and a ████ ███████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ for ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (that is, ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠), it ███████ that █████ ████ ███████ is ████ a █████ ███████ of the ████ ███████ as ███████. ██████, ███ has

█████████, the ████ ████████ is ████ a █████ ████████:

█████ ███████ do not ████ if ███ of █████ ██████ (█████████████, █████████ of ████ ████████ and █████████ of ████ ███████) is ███████. For a █████████ with a ██████ ██████████ (like a █████████) ███ ███ have, for ███████, that a ████ ████████ is not ███████████ a █████ ████████.

The ████ ██████ can be ████████ by ████ ████████ the █████████ of a █████ ████████ and a █████ ███████.

███████, ████ ████████ the █████████ of a ████ ████████ and a █████ ███████ (or ████ █████) is not ██████████ to ██████ a █████. For ███████, ████████ the ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$ with the ████████ ${\displaystyle \cdot }$ ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. This █████████ ████ have a ████ ████████ (██████, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠), and ████ ███████ has a █████ ███████ (which is ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for ████ ████████). ███████████, this █████████ is ███████████ (since the ███████ of ███ ██████ of ████████ is ██████ █████ to the █████████ ███████ in that ███████, ██████████ of the █████ in which █████ ██████████ are ███████). ███████, ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\cdot )}$ is not a █████, since it █████ a █████ ████████.

█████ █████████████

█████ █████████████ are █████████ that ███████ █████ █████████; they ███ be used to ██████ ███ ██████. A ████████████ from a █████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\cdot )}$ to a █████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\ast )}$ is a ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that

It █████ be ███████ to ███████ ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ ██████████, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, and ████████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(a^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(a{)}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ for ███ ${\displaystyle a}$ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. ███████, █████ ██████████ ████████████ ████ not be ████████ in the ██████████ of █████████████, because they are ███████ ███████ by the ███████████ of ██████████ the █████ █████████.

The ████████ ████████████ of a █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ that ████ ████ ███████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ██████. An ███████ ████████████ of a ████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, that is, ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. An ███████████ is a ████████████ that has an ███████ ████████████; ████████████, it is a █████████ ████████████. ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ██████ ██████████ if there ██████ an ███████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. In this ████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ can be ████████ from ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████ by ████████ ███ ████████ █████████ to the ████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠; ████ ███ █████████ ████ for ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████ for ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ████████ that ███ ████████ ████████ █████████ in the █████████ are ████ ███████.

The ██████████ of ███ ██████, ████████ with the █████████████ between ████, ████ a ████████, the ████████ of ██████.

An █████████ ████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ ███████████ as an ███████████ ████████ by an █████████, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }\stackrel{\sim }{\to }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\hookrightarrow \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for some ████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. █████████ █████████████ are the █████████████ in the ████████ of ██████.

█████████

██████████, a ████████ is a █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████████ within a ██████ ███, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠: it has a ██████ of the ████████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, with the ████ █████████. ██████████, this █████ that the ████████ ███████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ be █████████ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ are ████ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ████ ██ are ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, ██ the ████████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ████████ with the █████ █████████ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████████ to ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ██████ ████ a █████. In this ████, the █████████ ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ████████████.

In the ███████ of ██████████ of a ██████, the ████████ and the █████████ ██████████ a ████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\}}$⁠, ███████████ in ███ in the ██████ █████ of the ███████: ███ ███ █████████ ████████ are █████ a ████████, and a ████████ can be ██████ by (█.█., is ███████ to) the █████████████ █████████ ███° for ██°, ███° for ███°, and ██° for ███°. The ████████ ████ ████████ a █████████ and ██████████ █████████ for a ████████ ██████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ of a █████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ to be a ████████: it is ██████████ to █████ that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for ███ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. ███████ a █████'s █████████ is █████████ in █████████████ the █████ as a █████.

█████ ███ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of a █████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, the ████████ █████████ by ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ of ███ ████████ of ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and █████ ████████. It is the ████████ ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. In the ███████ of ██████████ of a ██████, the ████████ █████████ by ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ████████ of █████ ███ ████████, the ████████ ███████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and the ███████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠. █████, this is a ████████, because █████████ ███ ███ of █████ ████ ████████ or █████ ████████ (which are, in this ██████████ ████, █████ ████ ████████) ██████ an ███████ of this ████████.

██████

In ████ ██████████ it is █████████ to ████████ ███ █████ ████████ the ████ if they ██████ by an ███████ of a █████ ████████. For ███████, in the ████████ █████ of a ██████, ████ ███ ██████████ is █████████, █████████ █████ ██████ ██████ the ██████ to ███ ████████ ████████, ██ ███ can █████ of the █████████ █████████ of the ██████ as ███ being ██████████ to ████ █████, and as ████████████ to the ███████████ █████████; the ████████ ██████████ are ██████████ to the ████████ ███████ a ██████████ has been █████████. ██████ are used to █████████ this ███████: a ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████████ ████ and █████ ██████, which can be ███████ of as ████████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ by an █████████ █████ ███████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. In ████████ █████, the ████ and █████ ██████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ██████████ an ███████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, are

The ████ ██████ of ███ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ a █████████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠; that is, the █████ of ███ ████ ██████ is █████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ███ ████ ██████ are ██████ █████ or have an █████ ████████████. The █████ ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ █████████ ████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, █.█., ████ the ███ ████████ ██████ by an ███████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. ███████ ██████████████ █████ to the █████ ██████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. The ████ ██████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███ or ███ not be the ████ as ███ █████ ██████. If they are (that is, if ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠), ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████ to be a ██████ ████████.

In ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, the █████ of ██████████ of a ██████, with ███ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ of █████████, the ████ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ██████ █████ to ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, if ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is an ███████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████, or █████████ █████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\{{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\}}$ (███████████ in █████ in the ██████ █████ of ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠). The ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████, because ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and █████████ for the █████ ████████ of the █████. (In ████, in the ████ of ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠, the ██████ █████████ by ███████████ are ███ █████: ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠.)

████████ ██████

███████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ██████ ████████ of a █████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mid \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\}}$$ ███████ ███ ███ of ██████. ████ there is a ██████ █████ ███ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for which the ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ████████████. ██████████, the ███████ of ███ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ⁠${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, the █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ██████ as the ████████ of ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, and the ███████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in the ████████ █████ is ⁠${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\left({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\right)\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. The █████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠, ████ as "⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ ██████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠", is ██████ a ████████ █████ or ██████ █████. The ████████ █████ can █████████████ be █████████████ by a █████████ ████████.

The ████████ of the ████████ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. The █████ █████████ on the ████████ is █████ in the █████. For ███████, ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\cdot {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. ████ the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\}}$ and the ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ███████, but ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is not. █████████ a █████ can be █████████████ from a ████████ and ████████ (plus some ██████████ ████), by the ██████████ ███████ ████████████; ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is an ███████.

The █████ ███████████ ███████ ███████ that ███ ██████████ ████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ ███████████ as a ████████ ████████████ ████████ by an ███████████: ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}/\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\stackrel{\sim }{\to }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠. ██████████ █████████████ are the ████████████ in the ████████ of ██████.

█████████████

█████ █████ is ██████████ to a ████████ of a ████ █████, in ████ ████.

For ███████, the ████████ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is █████████ by the █████ ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and the ██████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ in a ████████ ████ (█████ ███████ of ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is a ██████ ███████ of ██████ of █████ and █████ ████████). █████ there is a ██████████ ████████████ ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ from the ████ █████ ${\displaystyle ⟨\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}⟩}$ on ███ ██████████ to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠. ████████ in ${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ██████ █████████; ████████ ███████ ⁠${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠. In ████, it █████ out that ${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████████ ██████ ████████ of ${\displaystyle ⟨\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}⟩}$ ██████████ █████ █████ ████████; in █████ █████, ███ █████████ are ████████████ of █████ █████. The ████████ of the ████ █████ by this ██████ ████████ is ███████ ⁠${\displaystyle ⟨\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mid {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}⟩}$⁠. This is ██████ a ████████████ of ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ by ██████████ and █████████, because the █████ ███████████ ███████ for ⁠${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$⁠ ██████ an ███████████ ⁠${\displaystyle ⟨\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mid {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cdot \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{)}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}⟩\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$⁠.

A ████████████ of a █████ can be used to █████████ the ██████ █████, a █████████ █████████ of a ████████ █████.