normalizedTrace_self_apply — Mathlib

English

Equality of the evaluation of the composed restrictions on an element x in K3, reflecting the tower structure.

Русский

Равенство значения композиции ограничений на элементе x из K3, отражающее структуру башни.

LaTeX

$$$\text{restrictNormalHom}_{K_1}(f) = (\text{restrictNormalHom}_{K_1})(\text{restrictNormalHom}_{K_2} f)$$$

Lean4

theorem normalizedTrace_self_apply (a : F) : normalizedTrace F F a = a :=
  by
  dsimp [normalizedTrace]
  rw [normalizedTraceAux_eq_of_fininteDimensional F a, Module.finrank_self F, Nat.cast_one, inv_one, one_smul,
    trace_self_apply]

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