Quantifier-free induction for lists

Stefan Hetzl; Jannik Vierling

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arXiv · 2305.08682

Quantifier-free induction for lists

Stefan Hetzl·Jannik Vierling

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Abstract

We investigate quantifier-free induction for Lisp-like lists constructed inductively from the empty list $\mathit{nil}$ and the operation $\mathit{cons}$, that adds an element to the front of a list. First we show that, for $m \geq 1$, quantifier-free $m$-step induction does not simulate quantifier-free $(m + 1)$-step induction. Secondly, we show that for all $m \geq 1$, quantifier-free $m$-step induction does not prove the right cancellation property of the concatenation operation on lists defined by left-recursion.

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BibTeX RIS

Stefan Hetzl, Jannik Vierling. 2023-05-15. Quantifier-free induction for lists. https://arxiv.org/abs/2305.08682

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