Category:Proof by Superinduction

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This category contains pages concerning Proof by Superinduction:


Let $A$ be a class.

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

Let $A$ be minimally superinductive under $g$.


Let $P: A \to \set {\T, \F}$ be a propositional function on $A$.

Suppose that:

\((1)\)   $:$   \(\ds \map P \O = \T \)      
\((2)\)   $:$     \(\ds \forall x \in A:\) \(\ds \map P x = \T \implies \map P {\map g x} = \T \)      
\((3)\)   $:$     \(\ds \forall C: \forall x \in C:\) \(\ds \map P x = \T \implies \map P {\bigcup C} = \T \)      where $C$ is a chain of elements of $A$


Then:

$\forall x \in A: \map P x = \T$

Pages in category "Proof by Superinduction"

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