projection_isIdempotentElem — Mathlib

English

The IsCompl projection hpq is idempotent (reiterated).

Русский

Проекция IsCompl hpq продолжает быть идемпотентной.

LaTeX

$$IsIdempotentElem (Submodule.IsCompl.projection hpq)$$

Lean4

/-- The linear projection onto a subspace along its complement is an idempotent. -/
@[simp]
theorem projection_isIdempotentElem (hpq : IsCompl p q) : IsIdempotentElem hpq.projection :=
  LinearMap.ext fun _ ↦ congr($(linearProjOfIsCompl_isCompl_projection hpq _))

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