Bandits.UCB.constSum_nonneg🔗

0 ≤ constSum c n

The type `ℝ` of real numbers constructed as equivalence classes of Cauchy sequences of rational
numbers.

The natural numbers, starting at zero.

This type is special-cased by both the kernel and the compiler, and overridden with an efficient
implementation. Both use a fast arbitrary-precision arithmetic library (usually
[GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.

The less-equal relation: `x ≤ y` 

Conventions for notations in identifiers:

 * The recommended spelling of `≤` in identifiers is `le`.

A sum that appears in the UCB regret upper bound. For `c > 2` it is bounded uniformly in `n`,
see `constSum_le`.

lemma constSum_nonneg (c : ℝ) (n : ℕ) : 0 ≤ constSum c n

Finset.sum_nonneg fun _ _ ↦ by positivity

New in v4.34.0-rc2-90-gdde3322 (2026-09-16), and its meaning has not changed since.

Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file · open it in the Lean web editor.

Dependency graph

Audit surface: 1 project declarations, 27 external constants

✓ Proved: no sorry anywhere in its closure

This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.