expUnitary — Mathlib

English

If a and b are self-adjoint and commute in A, then expUnitary(a) and expUnitary(b) commute.

Русский

Если a и b — самоприводные и коммутируют в A, то expUnitary(a) и expUnitary(b) commute.

LaTeX

$$$$\operatorname{Commute}(\expUnitary(a), \expUnitary(b))$$$$

Lean4

theorem expUnitary {a b : selfAdjoint A} (h : Commute (a : A) (b : A)) : Commute (expUnitary a) (expUnitary b) :=
  calc
    selfAdjoint.expUnitary a * selfAdjoint.expUnitary b = selfAdjoint.expUnitary b * selfAdjoint.expUnitary a := by
      rw [← h.expUnitary_add, ← h.symm.expUnitary_add, add_comm]

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