equiv — Mathlib

English

If J ≃ I is an equivalence, then OrthogonalIdempotents (e ∘ i) is equivalent to OrthogonalIdempotents e.

Русский

Если J эквивалентно I, то OrthogonalIdempotents (e ∘ i) эквивалентно OrthogonalIdempotents e.

LaTeX

$$OrthogonalIdempotents (e ∘ i) ↔ OrthogonalIdempotents e$$

Lean4

theorem equiv {J} [Fintype J] (i : J ≃ I) : CompleteOrthogonalIdempotents (e ∘ i) ↔ CompleteOrthogonalIdempotents e :=
  by
  simp only [completeOrthogonalIdempotents_iff, OrthogonalIdempotents.equiv, Function.comp_apply,
    Fintype.sum_equiv i _ e (fun _ ↦ rfl)]

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