Inductive base := 
  Undef | Def (f : {finMap K -> V}) of all p (supp f).Inductive base := 
  Undef | Def (f : {finMap K -> V}) of all p (supp f).Inductive base := 
  Undef | Def (f : {finMap K -> V}) of all p (supp f).

Lemma all_supp_remP k : all p (supp f) -> all p (supp (rem k f)).