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"
This category contains only the following page.