Module SSWP := WPropertiesOn SetOfSetsOfPositiveOrderedType SS.Module SSWEqP := WEqPropertiesOn SetOfSetsOfPositiveOrderedType SS.Module Import PosSort := Sort PosOrder.Definition pick_variety_auxCP {m : nat} (s : SS.elt) (cp : cartesianPower positive (S (S m))) : bool.Definition pick_variety_aux (s : SS.elt) (t : tST) := pick_variety_auxCP s t.

Lemma pick_variety_auxCP_existsF {m : nat} : forall s (cp : cartesianPower positive (S (S m))), pick_variety_auxCP s cp = false <-> (exists p, InCP p cp /\ S.mem p s = false).