Structural and (Noetherian) cyclic induction are two instances of the Noetherian induction
principle adapted to reason on first-order logic. From a theoretical point of view, every …

Cyclic induction is a powerful reasoning technique that consists in blocking the proof
development of certain subgoals already encountered during the proof process. In the …

A cyclic proof system, called CLKID-omega, gives us another way of representing inductive
definitions and efficient proof search. The 2011 paper by Brotherston and Simpson showed …

In first-order logic, the formula-based instances of the Noetherian induction principle allow to
perform effectively simultaneous, mutual and lazy induction reasoning. Compared to the …

A cyclic proof system, called CLKID-omega, gives us another way of representing inductive
definitions and efficient proof search. The 2005 paper by Brotherston showed that the …

We show how an inductive hypothesis can be inverted with small proof terms, using just
dependent elimination with a diagonal predicate. The technique works without any auxiliary …

CLKID^ ω ω is a sequent-based cyclic inference system able to reason on first-order logic
with inductive definitions. The current approach for verifying the soundness of CLKID^ ω ω …

We present a short implementation of the well-known Tortoise and Hare cycle finding
algorithm in the constructive setting of Coq. This algorithm is interesting from a constructive …

A cyclic proof system, called CLKID-omega, gives us another way of representing inductive
definitions and efficient proof search. The 2005 paper by Brotherston showed that the …

Cyclic proof provides a style of proof for logics with inductive (and coinductive) definitions, in
which proofs are cyclic graphs representing a form of argument by infinite descent. It is …