Theorems · Theorem · functional analysis

LinearIsometryEquiv.ofSurjective.congr_simp

∀ {R : Type u_1} {R₂ : Type u_2} {E₂ : Type u_6} {F : Type u_9} [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 E₂] [inst_5 : Module R₂ E₂] [inst_6 : NormedAddCommGroup F] [inst_7 : Module R F]
  (f f_1 : F →ₛₗᵢ[σ₁₂] E₂) (e_f : f = f_1) (hfr : Function.Surjective ⇑f),
  LinearIsometryEquiv.ofSurjective f hfr = LinearIsometryEquiv.ofSurjective f_1 ⋯

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

0 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairSeminormedAddCommGroupModuleNormedAddCommGroupModule