refl_symm — Mathlib

English

For any e: M1 ≃SL[σ₁₂] M2, the composition (as functions) of e with its inverse is the identity.

Русский

Для любого e: M1 ≃SL[σ₁₂] M2 композиция e с обратным e.symm равна тождественной функции.

LaTeX

$$$ (e : M_1 \\to M_2) \\circ (e^{-1} : M_2 \\to M_1) = \\mathrm{id}_{M_1} $$$

Lean4

@[simp]
theorem refl_symm : (ContinuousLinearEquiv.refl R₁ M₁).symm = ContinuousLinearEquiv.refl R₁ M₁ :=
  rfl

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