lookup-ne-implies-index-ne
update/>-inversion*
update-commutes-shift-converse*
fresh-update-implies-shift changed
join/<-inversion*
lookup-update-left-implies-unit-join
join-commute-update...
fresh-update-preserves-...-join-converse
disjoint-join-...-preserves-leq-converse
join-preserves-allrelation
Stray start of theorem removed.