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Diffstat (limited to 'mathcomp/algebra/ssrnum.v')
| -rw-r--r-- | mathcomp/algebra/ssrnum.v | 5 |
1 files changed, 5 insertions, 0 deletions
diff --git a/mathcomp/algebra/ssrnum.v b/mathcomp/algebra/ssrnum.v index 6198b44..45cd336 100644 --- a/mathcomp/algebra/ssrnum.v +++ b/mathcomp/algebra/ssrnum.v @@ -2016,6 +2016,11 @@ Lemma ler_sum I (r : seq I) (P : pred I) (F G : I -> R) : \sum_(i <- r | P i) F i <= \sum_(i <- r | P i) G i. Proof. exact: (big_ind2 _ (lexx _) ler_add). Qed. +Lemma ler_sum_nat (m n : nat) (F G : nat -> R) : + (forall i, (m <= i < n)%N -> F i <= G i) -> + \sum_(m <= i < n) F i <= \sum_(m <= i < n) G i. +Proof. by move=> le_FG; rewrite !big_nat ler_sum. Qed. + Lemma psumr_eq0 (I : eqType) (r : seq I) (P : pred I) (F : I -> R) : (forall i, P i -> 0 <= F i) -> (\sum_(i <- r | P i) (F i) == 0) = (all (fun i => (P i) ==> (F i == 0)) r). |