Talk:Church–Rosser theorem

Distinct vs possibly empty sequence of reductions
We say, "The Church–Rosser theorem states that if there are two distinct reductions starting from the same lambda calculus term, then there exists a term that is reachable via a (possibly empty) sequence of reductions from both reducts."

If the reducts are distinct, how can there exist a term that is reachable by an empty sequence of reductions? &mdash; Matt Crypto 09:20, 26 September 2009 (UTC)
 * What's the problem?  Two distinct reductions could end at the same term.  Or two reductions could end at terms a and b where b can be reduced to a by further reductions; then the common reachable term is a, and the reduction sequence from a is empty.


 * The only misstatement I see is grammatical; it should say "from each reduct". —Dominus (talk) 00:59, 28 September 2009 (UTC)