dual_eq_zero_iff — Mathlib

English

Compatibility of traceDual with equivalences under IsFractionRing: map_equiv_traceDual holds.

Русский

Совместимость traceDual с эквивалентностями под IsFractionRing: map_equiv_traceDual выполняется.

LaTeX

$$map_equiv_traceDual (I) : (traceDual A (FractionRing A) I).map (FractionRing.algEquiv B L) = traceDual A K (I.map (FractionRing.algEquiv B L)).$$

Lean4

@[simp]
theorem dual_eq_zero_iff : dual A K I = 0 ↔ I = 0 :=
  ⟨not_imp_not.mp (dual_ne_zero A K), fun e ↦ e.symm ▸ dual_zero A K L B⟩

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