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norm_id
simp
1 parent 2050ca5 commit 2d105a2Copy full SHA for 2d105a2
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Mathlib/Analysis/Normed/Operator/Basic.lean
@@ -321,6 +321,7 @@ theorem opNorm_add_le : ‖f + g‖ ≤ ‖f‖ + ‖g‖ :=
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(norm_add_le_of_le (f.le_opNorm x) (g.le_opNorm x)).trans_eq (add_mul _ _ _).symm
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/-- If a normed space is (topologically) non-trivial, then the norm of the identity equals `1`. -/
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+@[simp]
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theorem norm_id [NontrivialTopology E] : ‖ContinuousLinearMap.id 𝕜 E‖ = 1 :=
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le_antisymm norm_id_le <| by
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let ⟨x, hx⟩ := exists_norm_ne_zero E
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