projKerOfRightInverse_apply_idem — Mathlib

English

The subtraction of CLMs corresponds to subtraction of ContinuousAddMonoidHom structures.

Русский

Разность CLM соответствует разности структур ContinuousAddMonoidHom.

LaTeX

$$↑(f - g) = (f - g : ContinuousAddMonoidHom M M₂)$$

Lean4

@[simp]
theorem projKerOfRightInverse_apply_idem [IsTopologicalAddGroup M] (f₁ : M →SL[σ₁₂] M₂) (f₂ : M₂ →SL[σ₂₁] M)
    (h : Function.RightInverse f₂ f₁) (x : LinearMap.ker f₁) : f₁.projKerOfRightInverse f₂ h x = x :=
  by
  ext1
  simp

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