████████ ██████

██████████

A ████████ ${\displaystyle \mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████████ of the following █████ ████████████ ████████:

• A █████ ${\displaystyle \text{<span word-length="2" class="word redacted">██</span>}(\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, █████ ████████ are ██████ ███████;
• A █████ ${\displaystyle \text{<span word-length="3" class="word redacted">███</span>}(\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, █████ ████████ are ██████ █████████ or ████ or ██████.

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

  The ██████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:a\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ █████ be ████████ ██████ as "${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ is a ████████ from a to █".

  The ██████████ ${\displaystyle \text{<span word-length="3" class="word redacted">███</span>}(a,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ – █████████████ █████████ as ${\displaystyle {\text{<span word-length="3" class="word redacted">███</span>}}_{\mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}}(a,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, ${\displaystyle \text{<span word-length="3" class="word redacted">███</span>}(a,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$, or ${\displaystyle \mathcal{<span\; word-length="1"\; class="word\; redacted">█</span>}(a,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$ – ███████ the ███-█████ of ███ █████████ from ${\displaystyle a}$ to ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$.

• A ██████ █████████ ${\displaystyle \circ }$, ██████ ███████████ of █████████, ████ that for ███ █████ ███████ a, █, and █, ██ have$${\displaystyle \circ :\text{<span word-length="3" class="word redacted">███</span>}(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>},\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\times \text{<span word-length="3" class="word redacted">███</span>}(a,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\to \text{<span word-length="3" class="word redacted">███</span>}(a,\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})}$$The ███████████ 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 ███████ as ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ or ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ████████ by ███ ██████:
  1. █████████████: If ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:a\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, and ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ ████ $${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ (\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})=(\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>})\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$$
  2. ████████: For █████ ██████ █, there ██████ a ████████ ${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}:\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$ (████ ███████ as ${\displaystyle {\text{<span word-length="2" class="word redacted">██</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}}$) ██████ the ████████ ████████ for █, ████ that for █████ ████████ ${\displaystyle \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}:a\to \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}$, ██ have$${\displaystyle {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_{\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}\circ \mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}=\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}\circ {\mathrm{<span\; word-length="1"\; class="word\; redacted">█</span>}}_a}$$

     From the ██████, it can be ██████ that there is ███████ ███ ████████ ████████ for █████ ██████.

█████████

█████████ among █████████ (████ as ██ = █) are █████ ████████ using ███████████ ████████, with "██████" (███████) ████████████ ███████ and "██████" ████████████ █████████.

█████████ can have ███ of the following ██████████. A ████████ █ : a → █ is:

• a ████████████ (or █████) if █ ∘ █_█ = █ ∘ █_█ ███████ █_█ = █_█ for ███ █████████ █_█, █_█ : █ → a.
• an ███████████ (or ████) if █_█ ∘ █ = █_█ ∘ █ ███████ █_█ = █_█ for ███ █████████ █_█, █_█ : █ → █.
• a ██████████ if █ is ████ ████ and █████.
• an ███████████ if there ██████ a ████████ █ : █ → a ████ that █ ∘ █ = █_█ and █ ∘ █ = █_a.
• an ████████████ if a = █. ███(a) ███████ the █████ of █████████████ of a.
• an ████████████ if █ is ████ an ████████████ and an ███████████. ███(a) ███████ the █████ of █████████████ of a.
• a ██████████ if a █████ ███████ of █ ██████, █.█. if there ██████ a ████████ █ : █ → a with █ ∘ █ = █_█.
• a ███████ if a ████ ███████ of █ ██████, █.█. if there ██████ a ████████ █ : █ → a with █ ∘ █ = █_a.

█████ ██████████ is an ███████████, and █████ ███████ is a ████████████. ███████████, the following █████ ██████████ are ██████████:

• █ is a ████████████ and a ██████████;
• █ is an ███████████ and a ███████;
• █ is an ███████████.