diff --git a/Mathlib/Analysis/Normed/Group/Basic.lean b/Mathlib/Analysis/Normed/Group/Basic.lean index e3f93fb40be9b..f178ece3bbe0e 100644 --- a/Mathlib/Analysis/Normed/Group/Basic.lean +++ b/Mathlib/Analysis/Normed/Group/Basic.lean @@ -1096,12 +1096,12 @@ theorem comap_norm_nhds_one : comap norm (𝓝 0) = 𝓝 (1 : E) := by #align comap_norm_nhds_zero comap_norm_nhds_zero /-- Special case of the sandwich theorem: if the norm of `f` is eventually bounded by a real -function `a` which tends to `0`, then `f` tends to `1`. In this pair of lemmas (`squeeze_one_norm'` -and `squeeze_one_norm`), following a convention of similar lemmas in `Topology.MetricSpace.Basic` -and `Topology.Algebra.Order`, the `'` version is phrased using "eventually" and the non-`'` version -is phrased absolutely. -/ +function `a` which tends to `0`, then `f` tends to `1` (neutral element of `SeminormedGroup`). +In this pair of lemmas (`squeeze_one_norm'` and `squeeze_one_norm`), following a convention of +similar lemmas in `Topology.MetricSpace.Basic` and `Topology.Algebra.Order`, the `'` version is +phrased using "eventually" and the non-`'` version is phrased absolutely. -/ @[to_additive "Special case of the sandwich theorem: if the norm of `f` is eventually bounded by a -real function `a` which tends to `0`, then `f` tends to `1`. In this pair of lemmas +real function `a` which tends to `0`, then `f` tends to `0`. In this pair of lemmas (`squeeze_zero_norm'` and `squeeze_zero_norm`), following a convention of similar lemmas in `Topology.MetricSpace.PseudoMetric` and `Topology.Algebra.Order`, the `'` version is phrased using \"eventually\" and the non-`'` version is phrased absolutely."]