Follow-up from "Lang lemmas": intuitive explanation of mixin_step_by_val
"Let [fill K e1] and [fill K' e1'] be two decompositions of the same expression such that [e1'] is reducible. Then either [K] is a prefix of [K'] (so [e1] actually contains [e1'] as its head redex), or [e1] is a value. In other words, there cannot be two entirely unrelated head redexes that actually reduce."
@amintimany had an objection that I did not understand:
This does not really say anything about there not being redxes!
Of course it does? If there are redexes, the contexts are related; thus if there are unrelated contexts, there are no redexes.