norm_add_eq_iff_real

∀ {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] {x y : F},
  ‖x + y‖ = ‖x‖ + ‖y‖ ↔ ‖y‖ • x = ‖x‖ • y

Equality is achieved in the triangle inequality iff the two vectors are collinear.

Defined in: Mathlib.Analysis.InnerProductSpace.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup InnerProductSpace

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