█████ (████████ ██████)

██████ ███████████

The ██████ ███████████ █████, for a █████ █████ █ ██████ from the ██████████

${\displaystyle (-{)}^{\ast }:{\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\rightleftarrows {\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:(-{)}^{\ast }}$

█████ ████ ████████ are █████ by ███████ a ██████ █████ █ to ███ ████ ██████ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\ast }:=\mathrm{<span\; word-length="3"\; class="word\; redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$. The ██████████ █████ █████ a ██████ █████ █ to ███ ██████ ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\ast \ast }}$. This █████ is █████████, in ████ ███████ ██████████, by ████ (████).

███████ █████████ on █████████ ███████ ████

For ██████████ ███████ from █████████ ███████ ████ ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\le )}$ (with a ██████ ████████ from ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ if and ████ if ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\le \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$), ████ the █████████ ███████ ████ ███████: ███████ █████ are ██████ ███████████ and ██████ are ███████ █████████.

████-█████████ ███████████

For ███████, ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ be the █████████ ███████ from the ████████ ███ of ██████ to the ████████ ███ of ████, and ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ be the ████ █████ ███████ from the ████████ of ████ to the ████████ of ██████. ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is ████ ███████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. In this ████, the ██████████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ███████ the ██████████ ███ of the ████ █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$. The ████ ███ of this █████ is █████ by the ████

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

█████████ ███ ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ into the ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ in the ███████ ███, as ███████ of ██████ █. ███████, the ██████████████ of this █████ is the ███

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

████ out of a ███████ █████████████ or '██████████' of '███████ of ███████'. This ███████ to ███ ███████ ███████████████. The █████████ ███████ about ████ ██████ can be ███████████ to ███ ████ of ███████ in the █████ of a ███████ of ████████ in █████████ ███████. ████, █████ ████ ████ of ███████ █████ ████ to a █████ on the ████████ of ████. ███████████, the ███████ ████ can be █████████ from the █████ (as the ████████ of █████████–█████ ████████), ██ ██████ can ████ be ████ as ████████████ █████████ of █████████ ████████.

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

The █████ █████

The ███████████ of the █████ or ██████████ █████ ████ a ████████ █████:

${\displaystyle (-{)}_{\ast }:\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathbf{<span\; word-length="1"\; class="word\; redacted">█</span>}}$

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\cup \{\ast \}}$

The ████ is █████ by the █████████ of a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ into ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\ast }}$:

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

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

The ██████████████ ████ ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to ██████████, and the ███ ████████ ██████ in ${\displaystyle ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\ast }{)}_{\ast }}$ to the ███ in ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\ast }}$.

In ████ ██████████ ███████████ and ████████████ █████████, the █████ █████ ██████ ███████ ████████████, that is, ████████████ that ███ ████.

The █████ █████

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

The █████████ of the ████ at ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to the ████████

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

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

The ██████████████ ████ the ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}),\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto ({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime },{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime })}$ to the ████████

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

${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime }({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\prime })}$

In ████ ██████, █████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$ which is the ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})}$ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, ██ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}),{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}):\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$.

██ can ███████ █████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$ to ████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\to (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$. This in ████ can be █████ into ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ and ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ ██ that

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

████ ██ can ██-███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}))}$ as

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

██ can ███ ████ the ████ as ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}):\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\times \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$

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

In ██████████ ███████████ and ████████████ █████████, the █████ █████ ██████ ████████ ████████████.

The ███████████ █████

█████ a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, the ███████████ of the ██████ or ███████████ █████ ████ ████ ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to the ███ of █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. ████, the ███████████ of this █████ is ███████ the ███ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},-)}$. The █████████ of the ████ at ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ ████ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to the ████████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

The ██████████████ ████ a ███-████████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ to ███ "████████ █████████" ${\displaystyle (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mapsto \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})):\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. In █████ █████, ██████████████ is ██████████████ with

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

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

In ██████████ ███████████ and ████████████ █████████, the ███████████ █████ ██████ ████████████ with ██████ to some ████-████ ████.

The ████ and ███ ██████

The ████ or ██████████████ █████ ████ a ███ █ to the ███ of ██████ █████████ (█.█., █████) with ████████ from █. The ████ ████ an ███████ █ in █ to the █████████ ████ [█]. The ██████████████ ████████████ a ████ of █████ into a ██████ ████.

In ██████████ ███████████, the ████ █████ is used to █████ ████████████████ ████████████. The █████████ ████████ █████ is ████ █████ as the ███ █████, and is ████ used to █████ ████████████████ ███████████.

████████ over the ████ █████ █████

For ███████, for the ████ █████ █████ █████████ above, a ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-███████ is a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ with a ███ from the ████ █████ █████████ by ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ███████ to █████████████ and █████████ ██████████. ████ a █████████ is ██████████ to ██████ that ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a █████ ██████.

████████ over the ████████████ █████

███████ ███████ is the ████████████ █████ ${\displaystyle \mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ on the ████████ of ████. It is ███████ by ███████ a ███ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to the ███ of █████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ with ██████ ███████ and ████ that █████ ███ is █████ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. In ███-███████ ████████, this is the ███By ██████████ of the ███████████, it can be █████ that ████████ over the ████████████ █████ are ██████████ to ██████ ████, █.█., ████ ████████ with ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{+}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ for ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\in [\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}]}$ ███████ to ██████ ██████████ the ████████ of ██████ ██████ ████████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}+(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}-\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in █████████ █████.

████████ over the █████████ █████

███████ ██████ ███████ of a █████ is the █████████ ███████ ███████ on the ████████ of ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-███████ for a ███████████ ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.$${\displaystyle {\text{<span word-length="3" class="word redacted">███</span>}}^{\bullet }(-):\text{<span word-length="3" class="word redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\to \text{<span word-length="3" class="word redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$$███████ an ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-██████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ to the ██████ ███ of █████████ ██████ ██████$${\displaystyle {\text{<span word-length="3" class="word redacted">███</span>}}^{\bullet }(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\underset{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\overset{\mathrm{\infty }}{⨁}}{\text{<span word-length="3" class="word redacted">███</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$$█████ ${\displaystyle {\text{<span word-length="3" class="word redacted">███</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$. For ███████, ${\displaystyle {\text{<span word-length="3" class="word redacted">███</span>}}^{\bullet }({\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\oplus \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}})\cong \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}[{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}},\dots ,{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}]}$ █████ the ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-███████ on the █████ is ██████████ as a ██████. ████, an ███████ over this █████ are ███████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-████████. There are ████ ████████ over the ██████ for the ███████████ ███████ ${\displaystyle {\text{<span word-length="3" class="word redacted">███</span>}}^{\bullet }(-)}$ and █████ ██████ ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\bullet }(-)}$ ██████ ████-█████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-████████, and ████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-████████, ███████ the █████ ████ is the ████ ████-█████████ ███████ over ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-██████████ and the ██████ ████ is the ████ ███████ over ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ in ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-██████████.

███████████ ████████ in █-████████ ████ ███████

There is an █████████ ████████████ for ███████████ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-████████^{██ ███} which █████ ███████████ ${\displaystyle A}$-████████ for a ███████████ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-███████ ${\displaystyle A}$. If ${\displaystyle {\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}_A}$ is the ████████ of ${\displaystyle A}$-███████, ████ the ███████ ${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}:{\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}_A\to {\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}_A}$ :{\███████ {█}}█{A}\to {\███████ {█}}█{A}} is the █████ █████ by$${\displaystyle \mathbb{<span\; word-length="1"\; class="word\; redacted">█</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=\underset{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\ge \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}{\bigvee }{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}/{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$$█████$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}^{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}{\wedge }_A\cdots {\wedge }_A\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$$ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$-█████. ████ there is an ██████████ ████████ ${\displaystyle {\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}_A}$ of ███████████ ${\displaystyle A}$-████████ from the ████████ of ████████ over this █████.