Reducible element

Conjectura.Defs.ComputerScience.Rewriting.Reducible

/-
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 Mathlib.Logic.Relation

/-! # Reducible element

## 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 `x` is **reducible** under a relation `r` when some `y` satisfies `r x y` —
that is, at least one rewrite step applies to it. -/
def Reducible {α : Type*} (r : α → α → Prop) (x : α) : Prop := ∃ y, r x y

end Conjectura.Rewriting