inductive term : Type
| var  : nat → term
| app  : list term → term
| cnst : string → term

def var_of : term → option nat
| (term.var n) := some n
| _            := none

#check var_of.equations._eqn_1
#check var_of.equations._eqn_2
#check var_of.equations._eqn_3

def list_of : term → list term
| (term.app ts) := ts
| _             := []

#check list_of.equations._eqn_1
#check list_of.equations._eqn_2
#check list_of.equations._eqn_3

example (a : nat) (ls : list term) : term.var a = term.app ls → false :=
by contradiction

example (a : nat) (s : string) : ¬ term.var a = term.cnst s :=
by contradiction