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[Merged by Bors] - feat(Analysis/Normed/Group/Basic): add mem_closedBall_iff_nnnorm #43752

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[Merged by Bors] - feat(Analysis/Normed/Group/Basic): add mem_closedBall_iff_nnnorm #43752

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feat(Analysis/Normed/Group/Basic): add mem_closedBall_iff_nnnorm
b-mehta Sep 12, 2026
91f1dac
add mem_closedBall_iff_nnnorm' variant
b-mehta Sep 12, 2026
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8 changes: 8 additions & 0 deletions Mathlib/Analysis/Normed/Group/Basic.lean
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Expand Up @@ -869,6 +869,14 @@ theorem mem_closedBall_iff_norm'' : b ∈ closedBall a r ↔ ‖b / a‖ ≤ r :
theorem mem_closedBall_iff_norm''' : b ∈ closedBall a r ↔ ‖a / b‖ ≤ r := by
rw [mem_closedBall', dist_eq_norm_div]

@[to_additive mem_closedBall_iff_nnnorm]
theorem mem_closedBall_iff_nnnorm'' {r : ℝ≥0} : b ∈ closedBall a r ↔ ‖b / a‖₊ ≤ r :=
mem_closedBall_iff_norm''

@[to_additive mem_closedBall_iff_nnnorm']
theorem mem_closedBall_iff_nnnorm''' {r : ℝ≥0} : b ∈ closedBall a r ↔ ‖a / b‖₊ ≤ r :=
mem_closedBall_iff_norm'''

/-- A scaled closed ball is a closed ball. -/
@[to_additive setOf_sub_mem_closedBall_eq_closedBall
/-- A translated closed ball is a closed ball. -/]
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