Normal form

Conjectura.Defs.ComputerScience.Rewriting.Normal

/-
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
-/

import Conjectura.Defs.ComputerScience.Rewriting.Reducible

/-! # Normal form

## Source

Adapted for Conjectura from [cslib](https://github.com/leanprover/cslib), `Cslib/Foundations/Relation/Defs.lean`, split into one concept per module. Released by its authors under Apache 2.0.
-/

namespace Conjectura.Rewriting

/-- An element is in **normal form** when no rewrite step applies to it, i.e. it is not
`Reducible`. Normal forms are the possible end points of a computation. -/
def Normal {α : Type*} (r : α → α → Prop) (x : α) : Prop := ¬ Reducible r x

end Conjectura.Rewriting