End EqAllSigs.

(* Specifications: *)
Lemma big_allsigs (R : Type) (idx : R) (op : Monoid.law idx)
(I1 : Type)  (I2 : I1 -> Type)
(r1 : seq I1) (r2 : forall i1, seq (I2 i1)) (F : sigT I2 -> R) :
\big[op/idx]_(i <- [seq Tagged I2 i2 | i1 <- r1 & i2 <- r2 i1]) F i =
\big[op/idx]_(i1 <- r1) \big[op/idx]_(i2 <- r2 i1) F (Tagged I2 i2).