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Theorems · Definition · functional analysis

LinearIsometryEquiv.ofEq

{E : Type u_5} →
  [inst : SeminormedAddCommGroup E] →
    {R' : Type u_12} → [inst_1 : Ring R'] → [inst_2 : Module R' E] → (p q : Submodule R' E) → p = q → ↥p ≃ₗᵢ[R'] ↥q

LinearEquiv.ofEq as a LinearIsometryEquiv.

Defined in
Mathlib.Analysis.Normed.Operator.LinearIsometry
Cited by
7 results in Mathlib
Foundations
Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupRingModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LinearMap.normDet_comp · cited by 2LinearMap.normDet_compLinearMap.normDet_smul · cited by 1LinearMap.normDet_smulOrthonormalBasis.span · cited by 1OrthonormalBasis.spanLinearIsometryEquiv.ofEq.congr_simp · cited by 0ofEq.congr_simpOrthonormalBasis.span_apply · cited by 0OrthonormalBasis.span_app…LinearIsometryEquiv.ofEq_rfl · cited by 0LinearIsometryEquiv.ofEq_…LinearIsometryEquiv.ofEq_symm · cited by 0LinearIsometryEquiv.ofEq_…LinearIsometryEquiv.coe_ofEq_apply · cited by 0LinearIsometryEquiv.coe_o…Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idRing · cited by 7463RingSubmodule · cited by 7192SubmoduleLinearEquiv · cited by 3317LinearEquivSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupLinearIsometryEquiv · cited by 748LinearIsometryEquivLinearEquiv.ofEq · cited by 32LinearEquiv.ofEqLinearIsometryEquiv.ofEqCITED BYCITES

Cites8

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Cited by8

Results whose statement or proof uses this declaration.