Theorems · Theorem · functional analysis

LinearIsometryEquiv.injective

∀ {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} {σ₂₁ : R₂ →+* R} [inst_2 : RingHomInvPair σ₁₂ σ₂₁] [inst_3 : RingHomInvPair σ₂₁ σ₁₂]
  [inst_4 : SeminormedAddCommGroup E] [inst_5 : SeminormedAddCommGroup E₂] [inst_6 : Module R E] [inst_7 : Module R₂ E₂]
  (e : E ≃ₛₗᵢ[σ₁₂] E₂), Function.Injective ⇑e

Defined in

Mathlib.Analysis.Normed.Operator.LinearIsometry

Cited by

8 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairSeminormedAddCommGroupSeminormedAddCommGroupModuleModule