Definition ptr_ordMixin := OrdMixin ltn_ptr_irr ltn_ptr_trans ltn_ptr_total.Canonical ptr_ordType := OrdType ptr ptr_ordMixin.Inductive heap := 
  Undef | Def (finmap : {finMap ptr -> dynamic id}) of 
               null \notin supp finmap.Inductive heap := 
  Undef | Def (finmap : {finMap ptr -> dynamic id}) of 
               null \notin supp finmap.Inductive heap := 
  Undef | Def (finmap : {finMap ptr -> dynamic id}) of 
               null \notin supp finmap.

Lemma free_nullP : null \notin supp f -> null \notin supp (rem x f).