forall₂_true_iff — Mathlib

English

For any family β: α → Sort*, the statement ∀ a, β(a) → True is equivalent to True.

Русский

Для любой семейства β: α → Sort* утверждение ∀ a, β(a) → True эквивалентно True.

LaTeX

$$$$\\forall a, (\\beta(a) \\to True) \\iff True$$$$

Lean4

theorem forall₂_true_iff {β : α → Sort*} : (∀ a, β a → True) ↔ True := by
  simp
    -- This is not marked `@[simp]` because `implies_true : (α → True) = True` works

Похожие утверждения