dualAnnihilator_eq_bot_iff — Mathlib

English

With projectivity assumptions, W.dualAnnihilator = ⊥ iff W = ⊥ or W = ⊤ depending on context.

Русский

С предположениями проективности W.dualAnnihilator = ⊥ эквивалентно W = ⊥ или W = 0 в зависимости от контекста.

LaTeX

$$W.dualAnnihilator = ⊥ ↔ W = ⊥$$

Lean4

@[simp]
theorem dualAnnihilator_eq_bot_iff {W : Submodule R M} [Projective R (M ⧸ W)] : W.dualAnnihilator = ⊥ ↔ W = ⊤ := by
  rw [dualAnnihilator_eq_bot_iff', subsingleton_dual_iff, subsingleton_quotient_iff_eq_top]

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