> For the complete documentation index, see [llms.txt](https://adams-personal-organization.gitbook.io/compendium-of-predicates/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://adams-personal-organization.gitbook.io/compendium-of-predicates/definitions/non-preservation-of-extrema.md).

# Non-Preservation of Extrema

### Generative Effect

<details>

<summary><span class="math">\textbf{HasGenerativeEffect} \; A \; B \; R \; S \; f</span></summary>

***

$$\textbf{MonotoneMap} ; A ; B ; R ; S ; f$$

$$\exists( x,y \in A :: f(\sqcup {x,y}) ; \not \cong ; \sqcup {f.x, f.y })$$

***

```
pred HasGenerativeEffect(A,B: set univ, R,S,f: univ->univ) {
  MonotoneMap[A,B,R,S,f]
  some x,y: A {
    not Equivalent[
      B,S,
      f[Join[A,R,x+y]],
      Join[B,S,f[x]+f[y]]
    ]
  }
}
```

</details>