Church–Rosser property

ChurchRosserdef

A relation has the Church–Rosser property when any two elements connected by the equivalence it generates are Joinable. Equivalently: provable equality can always be decided by rewriting both sides.

def ChurchRosser {α : Type*} (r : α → α → Prop) : Prop :=
  ∀ ⦃a b : α⦄, Relation.EqvGen r a b → Joinable r a b

Builds on

Joinable elements

import Conjectura.Defs.ComputerScience.Rewriting.ChurchRosser · 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

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