Non-Preservation of Extrema

Generative Effect

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

---

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

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

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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]]
    ]
  }
}