████████ ██████

██████ and ████

In ████████ ██████ and █████████ ████████, the ████ "█████" ███████ a ███████████ █████. In █████ to █████ ███████████, ███ ██████ █████ with █████████ ██████; ███████, ███ ████████ ██████ to ████ █████ ███████████, ████ as being █████████ █████████ ████ █████████ or a ██ ███████.

In the ████ ████ as above, a "███" is a ██████████ ████████, ████████ with some █████ ███████████.

█████, ███ █████ with a ███████ █████—that is, a █████ with a "█████████████ █████", ██████ a █████████. A ███████ ███ is ████ a ███ which █████████ ██████████; that is, it █████ the █████████ of the ██████ to that of the ████████. In ████████, a ████ ███ is ███ which █████'█ ████████ ██████████.

The █████████ ███████ of ███ ███████ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are not █████████ ███████. A ██████████ is the █████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\wedge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ which is █████████████ by the ███████ ████████

${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\wedge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$,

that is, a █████ ███████ is an ██████ of a ██████ ███████ in ████████ ███████ (███ ██████-███ ██████████). ██████████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\wedge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ by the █████ ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\vee \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

████████

███ █ ██████ the ████ ████████ ${\displaystyle [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$. A ███

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$

is ██████ a ████████ from the ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ to the ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$. ███████████, ██ ███ █████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ as a ████ from the ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ to the ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. ██████, a ████████ can be █████ to be an ███████████ ████████. ████ █, █ are ███████ ██████, the ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ are ████████ to ████████ the █████████ and the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████ a █████ ████████. A █████ ████████ is the ████ as a (█████) ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\wedge {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{+}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{+}}$ is ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ with a ████████ █████████.

█████ a ███████ █████ █ and an ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=[{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ be the ████████ ███████ of █████ ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ from a (███████) █-██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ to █. As it █████ out,

• for ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ██████ ██████ ████████ ██████; in ██████████, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████ the ███████████ █████ of █,
• for ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ███████ ██████ by the ███████–██████ ████████,
• ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ can be ██████████ with the ███ of ████-█████████ ██████████ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

█████ █████ is the ███████████ █████ of some █████.

A ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████ a ████████ ███████████ if there is ███████ ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ are ████ █████████ to the ██████████. ███ ██████ are ████ to be ████████ ██████████ if there is a ████████ ███████████ between ████. A ████████ ███████████ █████ of ██████ is ████ ██████ a ████████ ████. There is a ██████ ██████: 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 ████ to be a ████ ████████ ███████████ if ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\ast }:{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ is an ███████████ for ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ████ ██████ of a ████ █████. A ████████ ███████████ is a ████ ████████ ███████████ but the ████████ ████ not be ████.

Through the ██████████

${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})),\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\cdot ))}$,

a ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is █████████ ██████ as a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$.

██ ███████

A ██ ███████ is a █████ that has a ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\supset \cdots \supset {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\supset {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\supset \cdots \supset {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ █████ is ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ████ that:

1. ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is a ████████ █████, ██████ the ███ of █-█████ (████████) in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.
2. ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ████████ by █████████ ███████ █-█████, █-█████, to ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ via ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$; █.█., the ████████ of an █-████ is ██████████ with the █████ of ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ in ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.
3. A ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████ if and ████ if ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cap {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is ████ for ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

For ███████, a ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ has ███ █████: ███ █-████ and ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-████, since ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ can be ████████ by ██████████ the ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ of the █-████ to a █████. In ███████, █████ ████████ has the ████████ ████ of a ██ ███████ (because a ████████ is an ████████ ████████████ ███████). ████ ██████████, █████ ██████ ███████ that a ███████ ████████ has the ████████ ████ of a ██████ ██ ███████.

██████████, █████████'s ███████ ████ that for ██ █████████, a ████ ████████ ███████████ and a ████████ ███████████ are the ████ █████.

███████ █████████ ██████ is the █████████████ ███████. █████, the ████████ ████████ of ██████ is the ████████ █████ an ██████ is a █████ but a ████████ is the ████████ █████ of a ███. ████

██████████, the above █████████████ ███████ can be ███████ as the ███████████ of the ████████ █████ ███████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\ast }}$ ████████ by the █████████ ███████████ ███████; ███ § ██████████ ███.

The above ███████ █████████ a ██████ █████ of ███████ ████ with ██ █████████. For ███████, █████ a █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ███ can ████ ██████ the ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to the ████████ of the ██ █████████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (the ████ █████████ of a ██ ███████ ██████████ the ███████ ████████, the ████████ ████████ and that can be █████ to be the ████████ of the ███████.)

█████████ on ██████, █████████ ██████ █████████████ ████████ ███ be █████████; █.█., ██████████ █████████████ or ██████ █████████████.

███████████ and █████████

A ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:A\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████ a ███████████ if █████:

1. A ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, and
2. A ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:A\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$

████ that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, there ██████ a ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ that ███████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ████ that ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. An ███████ is a ████████████ ███████████ ███████; that is, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ a ███████ ████████ ████████████ of a ██████ ████████ ${\displaystyle A}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ the █████████ (█.█., a ███████ ████████████ of a ██████ ███████████). In ████, a ███████████ can be █████████████ as a ████████████ ███████████ ███████ ████. ███████ █████ ███████ is a ██ ████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},A)}$; ████ █████ ████ ████ with ██ █████████ and the ██████ of a ███████████ there is ████ █████ ████████.

A █████████ in the █████ of ████████ is the ████ ██████ of a ███████████: that is, a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████████ if █████ (█) a ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and (█) a ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, there ██████ a ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ that ███████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ and ████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.

█████ a ███████████ is █████████████ by the █████████ of a ███████, a █████████ is █████████████ by the █████████ of a ███████ ██████ the ████ ███████ as ███████. ███ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ be the ████-████ of a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ along ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}):{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██████ the ███████ ████ █████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. ███████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }}$ as a ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (███ § ████████), if ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████████, ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }}$ █████ a ████████

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$

████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is █████ by ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. This ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ██████ the ████ ███████ ██████████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. ██████████, if there is a ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████████ as a ████████ ████████ is ████████ via ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

A █████ ███████ of a █████████ is a ████████ ███ as it █████ with a ██████ ████ ███████. If ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████████ █-██████ over a ███████████ █████, that is, a █████ with a ████ and ██████████ (███████████) █████ ██████ of a (███████████) █████, ████ the ██████████ ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████████, because a ████████ █████████ can be ███████ ███████ on a ███████████ █████.

█████ a ███████████ is █████████ with ██████ █████, a █████████ ████ not be ██████████.

There are ████ █████ ████████ of a ███████████ and a █████████ (██████, the ████ are ████████ to be █████).

███████ ████████

A ████ of ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:A\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████ to ███████ the ███████ ████████ if for ████ ███████████ ██████ ███████

there is a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ that █████ the above ███████ █████ ███████. (The ██████ ██████████ in the ██████ of █████ ██████████.)

███ ${\displaystyle \mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ be a █████ 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 ████ to ███████ the █████ ███████ ████████ or the ███ if ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████████ the above ███████ ████████ for ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. █████████, a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:A\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████ to ███████ the ████ ███████ ████████ or the ███ if it █████████ the ███████ ████████ for ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathfrak{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

For ███████, a ████████ █████████ 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 █████████ the ███ for the ██████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:A\to A\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. A █████ █████████ is a ███ ██████████ the ███ for the ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ is the █████ ███. A ████████ █████████ is a █████ █████████ and the ████████ █████ for ██ █████████.

On the █████ ████, a ███████████ is ███████ a ███ ██████████ the ███ for ██████████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ at ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

████ and ██████████

On the ████████ of ███████ ██████, there are ███ █████████ ████████: the ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and the (███████) ██████████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, which are in the ███████ ████████. █████████, they are ███████ as

• ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, and
• ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\wedge {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$.

Because of the ███████ ████████ between a █████ ███████ and a ███████ █████, ██ have:

${\displaystyle \mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}).}$

█████ ████████ are used to █████████ █████ █████████ and ███████ █████████. ██████, if ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ███, the █████ ████████ █████████ by ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the █████ ████████

${\displaystyle \cdots \to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$

█████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████████ █████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$; █.█., a █████ ████████ after █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ by a (█████) █████████. The ███████████ ████████ █████████ by ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \cdots ,}$ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is the ████████ ███████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████████ like a ████████ █████ (use a ████████ ███████ of a █████.)

The ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ to the ████████ of ██ █████████ in the following ████ █████: a ███████ of ██████ ████ that if ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ has the ████████ ████ of a ██ ███████, ████ ██ ████ ███ ████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

███████████ ██████ and ████████ ██████████

█████ a ███████████ █████ █, the ███████████ █████ for █████████ █-███████ ("the" up to ███████████) is a █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ that, for ████ █████ █,

${\displaystyle [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]=}$ {█████████ █-██████ on █} / ~ ${\displaystyle ,[\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]\mapsto [{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\ast }\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$

█████

• the ████-████ ████ is the ███ of ████████ ███████ of ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$,
• ~ ██████ ███████████ of ███████, and
• = is █████ by ███████-████ the █████████████ ██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ on ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (██████ █████████ ██████) along a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

█████'s ████████████████ ███████ ██████████ the █████████ of ███████████ ██████.

████████ and ███████████ ██████████

The ████ that a ███████████ █████ ██████████ █████████ ███████ can be ██████ ███████. For ███████, ███ █████ ███ to ████████ ██████████ ███████: █████ an ███████ █████ A (████ as ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$),

${\displaystyle [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})]={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>};A)}$

█████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(A,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ is the █████████–███████ █████. The above ████████ █████ to the ██████ of a ███████████ ██████████ ██████; █.█., a █████████████ ███████ from the ████████ of ██████ to the ████████ of ███████ ██████ that █████████ the ██████ ████████████ ████████ ██████████ ██████. As it █████ out, ████ a ███████ ███ not be █████████████ by a █████ but it can ██████ be ███████████ by a ████████ of (███████) ██████ with █████████ ████ ██████ a ████████. In █████ █████, to ████ a ███████████ ██████████ ██████ is to ████ a ████████. A █-██████ is an ███████ of a ███████████ ██████████ ██████.

A █████ ███████ of a ████████ is a ██████ ████████: ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to \cdots }$

████ ████████ and ██████ ████████

████████ ███████ and █████

████████ ██████ of ███████

█████ of ███, ██ have:

${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for .

This can be ████ by the ██████ or ██████████ █████████████ ███████. ██████, █████ a ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is █████████ to a ███ that is not ██████████ (███ the ████ ████████ are █████). But a ██████ with a █████ ███████ is ████████████.

███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ be the █████████ █████; ██████████, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$. ████, ██████ the ████ █████ ████████ of ████████ ██████, ██ ███

${\displaystyle \ast ={\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\ast }$

█████ █ is a █████. ████, ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\simeq {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, since █ is a ███████. Using the ████ ██████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$, by a ███████ ███████████, ██ ████ ███:

${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}.}$

█████████████, ██ can ████ use the ████████ ███████ to do ████████████.

████████ ██████ of ███ ██████

There is a ████████████ ██████ the █-████████████

${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\to {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}.}$