Category:Double Superinduction Principle

This category contains pages concerning Double Superinduction Principle:

Let $M$ be a class.

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

Let $\RR$ be a relation on $M$ which satisfies:

$(\text D_1)$	$:$	$\ds \forall x \in M:$	$\ds \map \RR {x, \O} $
$(\text D_2)$	$:$	$\ds \forall x, y \in M:$	$\ds \map \RR {x, y} \land \map \RR {y, x} \implies \map \RR {x, \map g y} $
$(\text D_3)$	$:$	$\ds \forall x \in M: \forall C: \forall y \in C:$	$\ds \map \RR {x, y} \implies \map \RR {x, \bigcup C} $	where $C$ is a chain of elements of $M$

Then $\map \RR {x, y}$ holds for all $x, y \in M$.

Pages in category "Double Superinduction Principle"

The following 3 pages are in this category, out of 3 total.

\((\text D_1)\)	$:$	\(\ds \forall x \in M:\)	\(\ds \map \RR {x, \O} \)
\((\text D_2)\)	$:$	\(\ds \forall x, y \in M:\)	\(\ds \map \RR {x, y} \land \map \RR {y, x} \implies \map \RR {x, \map g y} \)
\((\text D_3)\)	$:$	\(\ds \forall x \in M: \forall C: \forall y \in C:\)	\(\ds \map \RR {x, y} \implies \map \RR {x, \bigcup C} \)	where $C$ is a chain of elements of $M$