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[Merged by Bors] - chore(Algebra/Module/ZLattice/Summable): automated extraction from #39646 #40752

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[Merged by Bors] - chore(Algebra/Module/ZLattice/Summable): automated extraction from #39646 #40752

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4 changes: 1 addition & 3 deletions Mathlib/Algebra/Module/ZLattice/Summable.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -147,9 +147,7 @@ lemma sum_piFinset_Icc_rpow_le {ι : Type*} [Fintype ι] [DecidableEq ι]
rw [← Real.rpow_natCast, ← Real.rpow_add (by positivity), Nat.cast_sub hd]
norm_cast
_ ≤ 2 * d * 3 ^ (d - 1) * ε ^ r * ∑ k ∈ range (n + 1), (k : ℝ) ^ (d - 1 + r) := by
gcongr
rw [Finset.sum_range_succ', le_add_iff_nonneg_right]
positivity
grw [Finset.sum_range_succ', Nat.cast_zero, ← Real.rpow_nonneg le_rfl, add_zero]
_ ≤ 2 * d * 3 ^ (d - 1) * ε ^ r * ∑' k : ℕ, (k : ℝ) ^ (d - 1 + r) := by
gcongr
refine Summable.sum_le_tsum _ (fun _ _ ↦ by positivity) (Real.summable_nat_rpow.mpr ?_)
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