Instance frequencySizeMonotonic_alt :
forall {A : Type} (g0 : G A) (lg : seq (nat * G A)),
SizeMonotonic g0 ->
lg \subset [set x | SizeMonotonic x.2 ] ->
SizeMonotonic (frequency g0 lg).

Lemma forall_leq_sum_fst {A} (l : list (nat * A)) :
forall a n, seq_In l (n, a) -> n <= sum_fst l.