Category:General Double Induction Principle

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This category contains pages concerning General Double Induction Principle:


Let $M$ be a minimally inductive class under $g$.

Let $\RR$ be a relation which satisfies the following conditions:

\(({\text D'}_1)\)   $:$     \(\ds \forall x \in M:\)    \(\ds \map \RR {x, 0} \land \map \RR {0, x} \)   
\(({\text D'}_2)\)   $:$     \(\ds \forall x, y \in M:\)    \(\ds \paren {\map \RR {x, y} \land \map \RR {x, \map g y} \land \map \RR {\map g x, y} } \)   \(\ds \implies \)   \(\ds \map \RR {\map g x, \map g y} \)      


Then:

$\forall x, y \in M: \map \RR {x, y}$

Pages in category "General Double Induction Principle"

The following 2 pages are in this category, out of 2 total.