Real.sSup_nonpos

∀ {s : Set ℝ}, (∀ x ∈ s, x ≤ 0) → sSup s ≤ 0

As sSup s = 0 when s is an empty set of reals, it suffices to show that all elements of s are nonpositive to show that sSup s ≤ 0.

Defined in: Mathlib.Algebra.Order.Archimedean.Real.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

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