Set Implicit Arguments.
From Undecidability.HOU Require Import std.std calculus.calculus unification.unification.
From Undecidability.HOU Require Import third_order.pcp third_order.encoding.
Definition MPCP' '(c, C) :=
exists I, I ⊆ nats (length C) /\
hd c ++ @concat symbol (select I (heads C)) = tl c ++ concat (select I (tails C)).

Lemma MPCP_MPCP' c C: MPCP (c, C) <-> MPCP' (c, c::C).