bot_eq_zero — Mathlib

English

For a,b ∈ NNReal there exists a rational q with q ≥ 0 such that a < q.cast.toNNReal and q.cast.toNNReal < b.

Русский

Для a,b ∈ NNReal существует рациональный q с q ≥ 0 such that a < q.cast.toNNReal и q.cast.toNNReal < b.

LaTeX

$$$ \\forall a,b \\in NNReal, \\; a < b \\; \\iff \\; \\exists q \\in \\mathbb{Q}, 0 \\le q \\land a < q.cast.toNNReal \\land q.cast.toNNReal < b. $$$

Lean4

theorem bot_eq_zero : (⊥ : ℝ≥0) = 0 :=
  rfl

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