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 backtrackFuelSizeMonotonic {A : Type} tot fuel (lg : seq (nat * G (option A))) :
sum_fst lg = tot -> length lg = fuel ->
lg \subset [set x | SizeMonotonic x.2 ] ->
SizeMonotonic (backtrackFuel fuel tot lg).