instCoeTCContinuousLinearEquiv — Mathlib

English

The coercion from a LinearIsometryEquiv to its SL-notation is the identity on the underlying map.

Русский

Сублигированная карта из LinearIsometryEquiv в SL-представление совпадает с исходной функцией.

LaTeX

$$$ \big( e : E \to_{\sigma} E_2 \big) = e $$$

Lean4

/-- Reinterpret a `LinearIsometryEquiv` as a `ContinuousLinearEquiv`. -/
instance instCoeTCContinuousLinearEquiv : CoeTC (E ≃ₛₗᵢ[σ₁₂] E₂) (E ≃SL[σ₁₂] E₂) :=
  ⟨fun e => ⟨e.toLinearEquiv, e.continuous, e.toIsometryEquiv.symm.continuous⟩⟩

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