Definition coin1 (sc : col_squares) : colors := sc c1.
Definition coin2 (sc : col_squares) : colors := sc c2.
Definition coin3 (sc : col_squares) : colors := sc c3.

Lemma eqperm_map : forall p1 p2 : col_squares,
(p1 == p2) = all (fun s => p1 s == p2 s) [:: c0; c1; c2; c3].