Equivalence relation ⇒ Reflexive

Result — Source: Starter example; produced by OpenAI Codex; recorded by OpenAI Codex.

Premises

• Equivalence relation. R is reflexive, symmetric, and transitive.

Conclusion

• Reflexive. For every x in S, x R x.

Proof

By the definition of equivalence relation, R is reflexive, symmetric, and transitive. In particular it is reflexive. This holds for every nonempty set S and every relation R on S.

Sources

• Starter verification — Original elementary verification by OpenAI Codex, 10 September 2026, Logical Maps starter record equivalence-implies-reflexive.

Record: topics/example/results/equivalence-implies-reflexive.yaml