(* end randomSplitAssumption *)
CoInductive RandomSeedTree :=
| RstNode : RandomSeed -> RandomSeedTree -> RandomSeedTree -> RandomSeedTree.
Definition root_rst (rst : RandomSeedTree) : RandomSeed :=
match rst with
| RstNode root _ _ => root
end.
Definition left_rst (rst : RandomSeedTree) : RandomSeedTree :=
match rst with
| RstNode _ t1 _ => t1
end.
Definition right_rst (rst : RandomSeedTree) : RandomSeedTree :=
match rst with
| RstNode _ _ t2 => t2
end.

Lemma prefixFreeSingleton : forall p, PrefixFree [p].
intro.