diff --git a/CHANGELOG_UNRELEASED.md b/CHANGELOG_UNRELEASED.md index 118d8520c..017097a40 100644 --- a/CHANGELOG_UNRELEASED.md +++ b/CHANGELOG_UNRELEASED.md @@ -65,6 +65,8 @@ + `ball_le` - in `classical_sets.v`, lemma `bigcapCU` +- in `sequences.v`, lemmas `ler_sum_nat`, `sumr_const_nat` + ### Infrastructure ### Misc diff --git a/theories/sequences.v b/theories/sequences.v index 8a2f20cc8..292892e44 100644 --- a/theories/sequences.v +++ b/theories/sequences.v @@ -336,21 +336,6 @@ Lemma eq_sum_telescope (V : zmodType) (u_ : V ^nat) n : u_ n = u_ 0%N + series (telescope u_) n. Proof. by rewrite telescopeK/= addrC addrNK. Qed. -(* TODO: port to mathcomp *) -(* missing mathcomp lemmas *) -Lemma ler_sum_nat (R : numDomainType) (m n : nat) (F G : nat -> R) : - (forall i, (m <= i < n)%N -> (F i <= G i)%O) -> - (\sum_(m <= i < n) F i <= \sum_(m <= i < n) G i)%O. -Proof. -move=> leFG; rewrite big_nat_cond [in X in _ <= X]big_nat_cond. -by rewrite ler_sum// => i; rewrite andbT => /leFG. -Qed. - -Lemma sumr_const_nat (V : zmodType) (m n : nat) (x : V) : - \sum_(n <= i < m) x = x *+ (m - n). -Proof. by rewrite big_const_nat; elim: (m - n)%N => //= k ->; rewrite mulrS. Qed. -(* end missing mathcomp lemmas *) - Section series_patched. Variables (N : nat) (K : numFieldType) (V : normedModType K). @@ -1201,7 +1186,7 @@ Qed. Lemma ereal_limD (R : realType) (f g : nat -> {ereal R}) : cvg f -> cvg g -> ~~ adde_undef (lim f) (lim g) -> (lim (f \+ g) = lim f + lim g)%E. -Proof. +Proof. move=> cf cg fg; apply/(@cvg_lim _ _ ((f \+ g)%E @ \oo)) => //=. (* BUG *) exact: ereal_cvgD. Qed.