Theorems · Theorem · functional analysis

LinearIsometry.edist_map

∀ {R : Type u_1} {R₂ : Type u_2} {E : Type u_5} {E₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
  {σ₁₂ : R →+* R₂} [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup E₂] [inst_4 : Module R E]
  [inst_5 : Module R₂ E₂] (f : E →ₛₗᵢ[σ₁₂] E₂) (x y : E), edist (f x) (f y) = edist x y

Defined in

Mathlib.Analysis.Normed.Operator.LinearIsometry

Cited by

1 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringSeminormedAddCommGroupSeminormedAddCommGroupModuleModule