lean2/library/logic/classes/classes.md

logic.classes

Useful classes for general logical manipulations.

• inhabited : inhabited types
• nonempty : nonempty type
• decidable : decidable types
• congr : congruences with respect to suitable relations

Constructively, inhabited types have a witness, while nonempty types are "proof irrelevant". Classically (assuming the axiom in logic.axioms.hilbert) the two are equivalent. Type class inferences are set up to use "inhabited" however, so users should use that to declare that types have an element. Use "nonempty" in the hypothesis of a theorem when the theorem does not depend on the witness chosen.