Category:Relation on Slowly Progressing Mapping which fulfils conditions of General Double Induction Principle

This category contains pages concerning Relation on Slowly Progressing Mapping which fulfils conditions of General Double Induction Principle:

Let $M$ be a class.

Let $g: M \to M$ be a slowly progressing mapping on $M$.

Let $\map \RR {x, y}$ be the relation on $M$ defined as:

$\forall x, y \in M: \tuple {x, y} \in \R \iff x \subseteq y \lor y \subseteq x$

Then $\RR$ satisfies the conditions of the General Double Induction Principle:

$({\text D'}_1): \quad \map \RR {x, 0}$ and $\map \RR {0, x}$ hold for every $x \in M$

$({\text D'}_2): \quad \forall x, y \in M: \paren {\map \RR {x, y} \land \map \RR {x, \map g y} \land \map \RR {\map g x, y} } \implies \map \RR {\map g x, \map g y}$