Characteristics of Minimally Inductive Class under Progressing Mapping/Sandwich Principle/Proof 2
Jump to navigation
Jump to search
Theorem
Let $M$ be a class which is minimally inductive under a progressing mapping $g$.
Then for all $x, y \in M$:
- $x \subseteq y \subseteq \map g x \implies x = y \lor y = \map g x$
Proof
By definition of minimally inductive class, $M$ is minimally closed under $g$ with respect to $\O$.
The result is then seen to be a direct application of Sandwich Principle for Minimally Closed Class.
$\blacksquare$