Local confluence

LocallyConfluentdef

A relation is locally confluent when any two single steps out of a common element are Joinable. Weaker than Confluent; Newman's lemma says the two coincide for terminating relations.

def LocallyConfluent {α : Type*} (r : α → α → Prop) : Prop :=
  ∀ ⦃a b c : α⦄, r a b → r a c → Joinable r b c

Builds on

Joinable elements

import Conjectura.Defs.ComputerScience.Rewriting.LocallyConfluent · maintainer — open · raw source

Adapted for Conjectura from cslib, `Cslib/Foundations/Relation/Defs.lean`, split into one concept per module. Released by its authors under Apache 2.0.

Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson

Full credits